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Volumn 25, Issue 1, 1997, Pages 1-29

Stochastic models of interacting systems

Author keywords

Contact processes; Exclusion processes; Stochastic Ising model; Voter models

Indexed keywords


EID: 0031493470     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404276     Document Type: Article
Times cited : (69)

References (95)
  • 1
    • 51249162954 scopus 로고
    • Hammersley's interacting particle process and longest increasing subsequences
    • ALDOUS, D. and DIACONIS, P. (1995). Hammersley's interacting particle process and longest increasing subsequences. Probab. Theory Related Fields 103 199-213.
    • (1995) Probab. Theory Related Fields , vol.103 , pp. 199-213
    • Aldous, D.1    Diaconis, P.2
  • 2
    • 0001476349 scopus 로고
    • Uniqueness of stationary ergodic fixed point for a ·/M/k node
    • ANANTHARAM, V. (1993). Uniqueness of stationary ergodic fixed point for a ·/M/k node. Ann. Appl. Probab. 3 154-173.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 154-173
    • Anantharam, V.1
  • 3
    • 0039586360 scopus 로고
    • The contact process in high dimensions
    • ANDJEL, E. D. (1988). The contact process in high dimensions. Ann. Probab. 16 1174-1183.
    • (1988) Ann. Probab. , vol.16 , pp. 1174-1183
    • Andjel, E.D.1
  • 4
    • 51249168406 scopus 로고
    • Survival of multidimensional contact process in random environments
    • ANDJEL, E. D. (1992). Survival of multidimensional contact process in random environments. Bol. Soc. Brasil. Mat. 23 109-119.
    • (1992) Bol. Soc. Brasil. Mat. , vol.23 , pp. 109-119
    • Andjel, E.D.1
  • 7
    • 0001103678 scopus 로고
    • The critical contact process dies out
    • BEZUIDENHOUT, C. and GRIMMETT, G. (1990). The critical contact process dies out. Ann. Probab. 18 1462-1482.
    • (1990) Ann. Probab. , vol.18 , pp. 1462-1482
    • Bezuidenhout, C.1    Grimmett, G.2
  • 8
    • 0001047331 scopus 로고
    • The contact process in a random environment
    • BRAMSON, M., DURRETT, R. and SCHONMANN, R. H. (1991). The contact process in a random environment. Ann. Probab. 19 960-983.
    • (1991) Ann. Probab. , vol.19 , pp. 960-983
    • Bramson, M.1    Durrett, R.2    Schonmann, R.H.3
  • 9
    • 0021442334 scopus 로고
    • Metastable behavior of stochastic dynamics: A pathwise approach
    • CASSANDRO, M., GALVES, A., OLIVIERI, E. and VARES, M. E. (1984). Metastable behavior of stochastic dynamics: a pathwise approach. J. Statist. Phys. 35 603-628.
    • (1984) J. Statist. Phys. , vol.35 , pp. 603-628
    • Cassandro, M.1    Galves, A.2    Olivieri, E.3    Vares, M.E.4
  • 11
    • 0015723047 scopus 로고
    • A model for spatial conflict
    • CLIFFORD, P. and SUDBURY, A. (1973). A model for spatial conflict. Biometrica 60 581-588.
    • (1973) Biometrica , vol.60 , pp. 581-588
    • Clifford, P.1    Sudbury, A.2
  • 13
    • 0001127292 scopus 로고
    • Occupation time limit theorems for the voter model
    • COX, J. T. and GRIFFEATH, D. (1983). Occupation time limit theorems for the voter model. Ann. Probab. 11 876-893.
    • (1983) Ann. Probab. , vol.11 , pp. 876-893
    • Cox, J.T.1    Griffeath, D.2
  • 15
    • 0642277133 scopus 로고
    • Exact solution of the totally asymmetric simple exclusion process: Shock profiles
    • DERRIDA, B., JANOWSKY, S. A., LEBOWITZ, J. L. and SPEER, E. R. (1993). Exact solution of the totally asymmetric simple exclusion process: shock profiles. J. Statist. Phys. 73 813-842.
    • (1993) J. Statist. Phys. , vol.73 , pp. 813-842
    • Derrida, B.1    Janowsky, S.A.2    Lebowitz, J.L.3    Speer, E.R.4
  • 16
    • 0009813530 scopus 로고
    • Markov processes with a large number of locally interacting components: Existence of a limit process and its ergodicity
    • DOBRUSHIN, R. L. (1971a). Markov processes with a large number of locally interacting components: existence of a limit process and its ergodicity. Problems Inform. Transmission 7 149-164.
    • (1971) Problems Inform. Transmission , vol.7 , pp. 149-164
    • Dobrushin, R.L.1
  • 17
    • 0001697468 scopus 로고
    • Markov processes with many locally interacting components - The reversible case and some generalizations
    • DOBRUSHIN, R. L. (1971b). Markov processes with many locally interacting components - the reversible case and some generalizations. Problems Inform. Transmission 7 235-241.
    • (1971) Problems Inform. Transmission , vol.7 , pp. 235-241
    • Dobrushin, R.L.1
  • 18
    • 0000221088 scopus 로고
    • On the growth of one-dimensional contact processes
    • DURRETT, R. (1980). On the growth of one-dimensional contact processes. Ann. Probab. 8 890-907.
    • (1980) Ann. Probab. , vol.8 , pp. 890-907
    • Durrett, R.1
  • 21
    • 0002427482 scopus 로고
    • Stochastic growth models - Bounds on critical values
    • DURRETT, R. (1992a). Stochastic growth models - bounds on critical values. J. Appl. Probab. 29 11-20.
    • (1992) J. Appl. Probab. , vol.29 , pp. 11-20
    • Durrett, R.1
  • 22
    • 0001126078 scopus 로고
    • Multicolor particle systems with large threshold and range
    • DURRETT, R. (1992b). Multicolor particle systems with large threshold and range. J. Theoret. Probab. 5 127-152.
    • (1992) J. Theoret. Probab. , vol.5 , pp. 127-152
    • Durrett, R.1
  • 24
  • 25
    • 0009226667 scopus 로고
    • The contact process on a finite set
    • DURRETT, R. and LIU, X. (1988). The contact process on a finite set. Ann. Probab. 16 1158-1173.
    • (1988) Ann. Probab. , vol.16 , pp. 1158-1173
    • Durrett, R.1    Liu, X.2
  • 26
    • 0031285155 scopus 로고    scopus 로고
    • Coexistence results for some competition models
    • DURRETT, R. and NEUHAUSER, C. (1997). Coexistence results for some competition models. Ann. Appl. Probab. 7.
    • (1997) Ann. Appl. Probab. , vol.7
    • Durrett, R.1    Neuhauser, C.2
  • 27
    • 0000157884 scopus 로고
    • Intermediate phase for the contact process on a tree
    • DURRETT, R. and SCHINAZI, R. (1995). Intermediate phase for the contact process on a tree. Ann. Probab. 23 668-673.
    • (1995) Ann. Probab. , vol.23 , pp. 668-673
    • Durrett, R.1    Schinazi, R.2
  • 28
    • 0009144706 scopus 로고
    • The contact process on a finite set. II
    • DURRETT, R. and SCHONMANN, R. (1988). The contact process on a finite set. II. Ann. Probab. 16 1570-1583.
    • (1988) Ann. Probab. , vol.16 , pp. 1570-1583
    • Durrett, R.1    Schonmann, R.2
  • 29
    • 0039364564 scopus 로고
    • The contact process on a finite set. III. The critical case
    • DURRETT, R., SCHONMANN, R. and TANAKA, N. (1989). The contact process on a finite set. III. The critical case. Ann. Probab. 17 1303-1321.
    • (1989) Ann. Probab. , vol.17 , pp. 1303-1321
    • Durrett, R.1    Schonmann, R.2    Tanaka, N.3
  • 30
    • 0037836715 scopus 로고
    • Fixation results for threshold voter systems
    • DURRETT, R. and STEIF, J. E. (1993). Fixation results for threshold voter systems. Ann. Probab. 21 232-247.
    • (1993) Ann. Probab. , vol.21 , pp. 232-247
    • Durrett, R.1    Steif, J.E.2
  • 31
    • 0002191939 scopus 로고
    • Shock fluctuations in asymmetric simple exclusion
    • FERRARI, P. (1992). Shock fluctuations in asymmetric simple exclusion. Probab. Theory Related Fields 91 81-101.
    • (1992) Probab. Theory Related Fields , vol.91 , pp. 81-101
    • Ferrari, P.1
  • 32
    • 21344488955 scopus 로고
    • Shock fluctuations in the asymmetric simple exclusion process
    • FERRARI, P. and FONTES, L. R. G. (1994). Shock fluctuations in the asymmetric simple exclusion process. Probab. Theory Related Fields 99 305-319.
    • (1994) Probab. Theory Related Fields , vol.99 , pp. 305-319
    • Ferrari, P.1    Fontes, L.R.G.2
  • 33
    • 21844523675 scopus 로고
    • Invariant measures for a two-species asymmetric process
    • FERRARI, P., FONTES, L. R. G. and KOHAYAKAWA, Y. (1994). Invariant measures for a two-species asymmetric process. J. Statist. Phys. 76 1153-1177.
    • (1994) J. Statist. Phys. , vol.76 , pp. 1153-1177
    • Ferrari, P.1    Fontes, L.R.G.2    Kohayakawa, Y.3
  • 34
    • 0001623535 scopus 로고
    • Microscopic structure of travelling waves in the asymmetric simple exclusion process
    • FERRARI, P., KIPNIS, C. and SAADA, E. (1991). Microscopic structure of travelling waves in the asymmetric simple exclusion process. Ann. Probab. 19 226-244.
    • (1991) Ann. Probab. , vol.19 , pp. 226-244
    • Ferrari, P.1    Kipnis, C.2    Saada, E.3
  • 36
    • 0040771958 scopus 로고
    • A stability criterion for attractive nearest-neighbor spin systems on Z
    • GRAY, L. and GRIFFEATH, D. (1982). A stability criterion for attractive nearest-neighbor spin systems on Z. Ann. Probab. 10 67-85.
    • (1982) Ann. Probab. , vol.10 , pp. 67-85
    • Gray, L.1    Griffeath, D.2
  • 37
    • 0000129207 scopus 로고
    • Limit theorems for nonergodic set-valued Markov processes
    • GRIFFEATH, D. (1978). Limit theorems for nonergodic set-valued Markov processes. Ann. Probab. 6 379-387.
    • (1978) Ann. Probab. , vol.6 , pp. 379-387
    • Griffeath, D.1
  • 39
  • 40
    • 0039586356 scopus 로고
    • The binary contact path process
    • GRIFFEATH, D. (1983). The binary contact path process. Ann. Probab. 11 692-705.
    • (1983) Ann. Probab. , vol.11 , pp. 692-705
    • Griffeath, D.1
  • 41
    • 0001792547 scopus 로고
    • On the critical infection rate of the one-dimensional basic contact process: Numerical results
    • GRILLENBERGER, C. and ZIEZOLD, H. (1988). On the critical infection rate of the one-dimensional basic contact process: numerical results. J. Appl. Probab. 25 1-8.
    • (1988) J. Appl. Probab. , vol.25 , pp. 1-8
    • Grillenberger, C.1    Ziezold, H.2
  • 42
    • 0000042426 scopus 로고
    • Percolation in ∞ + 1 dimensions
    • Oxford Univ. Press
    • GRIMMETT, G. and NEWMAN, C. (1990). Percolation in ∞ + 1 dimensions. In Disorder in Physical Systems 167-190. Oxford Univ. Press.
    • (1990) Disorder in Physical Systems , pp. 167-190
    • Grimmett, G.1    Newman, C.2
  • 43
    • 0000829680 scopus 로고
    • Contact interactions on a lattice
    • HARRIS, T. E. (1974). Contact interactions on a lattice. Ann. Probab. 2 969-988.
    • (1974) Ann. Probab. , vol.2 , pp. 969-988
    • Harris, T.E.1
  • 44
    • 0000589180 scopus 로고
    • On a class of set-valued Markov processes
    • HARRIS, T. E. (1976). On a class of set-valued Markov processes. Ann. Probab. 4 175-194.
    • (1976) Ann. Probab. , vol.4 , pp. 175-194
    • Harris, T.E.1
  • 46
    • 84864351116 scopus 로고
    • On the asymptotics of the spin-spin autocorrelation function in stochastic ising models near the critical temperature
    • Birkhäuser, Boston
    • HOLLEY, R. (1991). On the asymptotics of the spin-spin autocorrelation function in stochastic Ising models near the critical temperature. In Spatial Stochastic Processes: a Festschrift in Honor of Ted Harris on His Seventieth Birthday 89-104. Birkhäuser, Boston.
    • (1991) Spatial Stochastic Processes: A Festschrift in Honor of Ted Harris on His Seventieth Birthday , pp. 89-104
    • Holley, R.1
  • 47
    • 0000550994 scopus 로고
    • Ergodic theorems for weakly interacting systems and the voter model
    • HOLLEY, R. and LIGGETT, T. M. (1975). Ergodic theorems for weakly interacting systems and the voter model. Ann. Probab. 3 643-663.
    • (1975) Ann. Probab. , vol.3 , pp. 643-663
    • Holley, R.1    Liggett, T.M.2
  • 48
    • 0000359562 scopus 로고
    • The survival of contact processes
    • HOLLEY, R. and LIGGETT, T. M. (1978). The survival of contact processes. Ann. Probab. 6 198-206.
    • (1978) Ann. Probab. , vol.6 , pp. 198-206
    • Holley, R.1    Liggett, T.M.2
  • 49
    • 0000407851 scopus 로고
    • Generalized potlatch and smoothing processes
    • HOLLEY, R. and LIGGETT, T. M. (1981). Generalized potlatch and smoothing processes. Z. Wahrsch. Verw. Gebiete 55 165-195.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.55 , pp. 165-195
    • Holley, R.1    Liggett, T.M.2
  • 50
    • 0001359676 scopus 로고
    • Logarithmic sobolev inequalities and stochastic Ising models
    • HOLLEY, R. and STROOCK, D. W. (1987). Logarithmic Sobolev inequalities and stochastic Ising models. J. Statist. Phys. 46 1159-1194.
    • (1987) J. Statist. Phys. , vol.46 , pp. 1159-1194
    • Holley, R.1    Stroock, D.W.2
  • 51
    • 0000578550 scopus 로고
    • Simulated annealing via Sobolev inequalities
    • HOLLEY, R. and STROOCK, D. W. (1988). Simulated annealing via Sobolev inequalities. Comm. Math. Phys. 115 553-569.
    • (1988) Comm. Math. Phys. , vol.115 , pp. 553-569
    • Holley, R.1    Stroock, D.W.2
  • 52
    • 0001912118 scopus 로고
    • 2 convergence in one dimensional stochastic Ising models
    • 2 convergence in one dimensional stochastic Ising models. Comm. Math. Phys. 123 85-93.
    • (1989) Comm. Math. Phys. , vol.123 , pp. 85-93
    • Holley, R.1    Stroock, D.W.2
  • 53
    • 0000061720 scopus 로고
    • Central limit theorems for infinite series of queues and applications to simple exclusion
    • KIPNIS, C. (1986). Central limit theorems for infinite series of queues and applications to simple exclusion. Ann. Probab. 14 397-408.
    • (1986) Ann. Probab. , vol.14 , pp. 397-408
    • Kipnis, C.1
  • 55
    • 84990617818 scopus 로고
    • Hydrodynamics and large deviation for simple exclusion processes
    • KIPNIS, C., OLLA, S. and VARADHAN, S. R. S. (1989). Hydrodynamics and large deviation for simple exclusion processes. Comm. Pure Appl. Math. 42 115-137.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 115-137
    • Kipnis, C.1    Olla, S.2    Varadhan, S.R.S.3
  • 56
    • 0010241049 scopus 로고
    • Extinction of contact and percolation processes in a random environment
    • KLEIN, A. (1994). Extinction of contact and percolation processes in a random environment. Ann. Probab. 22 1227-1251.
    • (1994) Ann. Probab. , vol.22 , pp. 1227-1251
    • Klein, A.1
  • 58
    • 0005273704 scopus 로고
    • Ergodic theorems for the asymmetric exclusion process
    • LIGGETT, T. M. (1975). Ergodic theorems for the asymmetric exclusion process. Trans. Amer. Math. Soc. 213 237-261.
    • (1975) Trans. Amer. Math. Soc. , vol.213 , pp. 237-261
    • Liggett, T.M.1
  • 59
    • 0001276925 scopus 로고
    • Coupling the simple exclusion process
    • LIGGETT, T. M. (1976). Coupling the simple exclusion process. Ann. Probab. 4 339-356.
    • (1976) Ann. Probab. , vol.4 , pp. 339-356
    • Liggett, T.M.1
  • 60
    • 0012497160 scopus 로고
    • Ergodic theorems for the asymmetric exclusion process. II
    • LIGGETT, T. M. (1977). Ergodic theorems for the asymmetric exclusion process. II. Ann. Probab. 5 795-801.
    • (1977) Ann. Probab. , vol.5 , pp. 795-801
    • Liggett, T.M.1
  • 63
    • 0001640370 scopus 로고
    • The survival of one-dimensional contact processes in random environments
    • LIGGETT, T. M. (1992). The survival of one-dimensional contact processes in random environments. Ann. Probab. 20 696-723.
    • (1992) Ann. Probab. , vol.20 , pp. 696-723
    • Liggett, T.M.1
  • 64
    • 0009222590 scopus 로고
    • Coexistence in threshold voter models
    • LIGGETT, T. M. (1994). Coexistence in threshold voter models. Ann. Probab. 22 764-802.
    • (1994) Ann. Probab. , vol.22 , pp. 764-802
    • Liggett, T.M.1
  • 65
    • 0001277458 scopus 로고
    • Improved upper bounds for the contact process critical value
    • LIGGETT, T. M. (1995a). Improved upper bounds for the contact process critical value. Ann. Probab. 23 697-723.
    • (1995) Ann. Probab. , vol.23 , pp. 697-723
    • Liggett, T.M.1
  • 66
    • 21844522564 scopus 로고
    • Survival of discrete time growth models, with applications to oriented percolation
    • LIGGETT, T. M. (1995b). Survival of discrete time growth models, with applications to oriented percolation. Ann. Appl. Probab. 5 613-636.
    • (1995) Ann. Appl. Probab. , vol.5 , pp. 613-636
    • Liggett, T.M.1
  • 67
    • 0030371517 scopus 로고    scopus 로고
    • Multiple transition points for the contact process on the binary tree
    • LIGGETT, T. M. (1996). Multiple transition points for the contact process on the binary tree. Ann. Probab. 24 1675-1710.
    • (1996) Ann. Probab. , vol.24 , pp. 1675-1710
    • Liggett, T.M.1
  • 68
    • 0039077812 scopus 로고    scopus 로고
    • Branching random walks and contact processes on homogeneous trees
    • To appear
    • LIGGETT, T. M. (1997). Branching random walks and contact processes on homogeneous trees. Probab. Theory Related Fields. To appear.
    • (1997) Probab. Theory Related Fields
    • Liggett, T.M.1
  • 69
    • 0010258563 scopus 로고
    • On the critical behavior of the contact process in deterministic inhomogeneous environment
    • MADRAS, N., SCHINAZI, R. and SCHONMANN, R. (1994). On the critical behavior of the contact process in deterministic inhomogeneous environment. Ann. Probab. 22 1140-1159.
    • (1994) Ann. Probab. , vol.22 , pp. 1140-1159
    • Madras, N.1    Schinazi, R.2    Schonmann, R.3
  • 70
    • 21344495600 scopus 로고
    • The critical contact process on a homogeneous tree
    • MORROW, G., SCHINAZI, R. and ZHANG, Y. (1993). The critical contact process on a homogeneous tree. J. Appl. Probab. 31 250-255.
    • (1993) J. Appl. Probab. , vol.31 , pp. 250-255
    • Morrow, G.1    Schinazi, R.2    Zhang, Y.3
  • 71
    • 0000108320 scopus 로고
    • A metastable result for the finite multidimensional contact process
    • MOUNTFORD, T. S. (1993). A metastable result for the finite multidimensional contact process. Canad. Math. Bull. 36 216-226.
    • (1993) Canad. Math. Bull. , vol.36 , pp. 216-226
    • Mountford, T.S.1
  • 72
    • 0001153989 scopus 로고
    • On the weak convergence of departures from an infinite series of ·/M/1 queues
    • MOUNTFORD, T. S. and PRABHAKAR, B. (1995) On the weak convergence of departures from an infinite series of ·/M/1 queues. Ann. Appl. Probab. 5 121-127.
    • (1995) Ann. Appl. Probab. , vol.5 , pp. 121-127
    • Mountford, T.S.1    Prabhakar, B.2
  • 73
    • 0030516627 scopus 로고    scopus 로고
    • Persistent survival of one-dimensional contact processes in random environments
    • NEWMAN, C. M. and VOLCHAN, S. B. (1996). Persistent survival of one-dimensional contact processes in random environments. Ann. Probab. 24 411-421.
    • (1996) Ann. Probab. , vol.24 , pp. 411-421
    • Newman, C.M.1    Volchan, S.B.2
  • 74
    • 0000771579 scopus 로고
    • The contact process on trees
    • PEMANTLE, R. (1992). The contact process on trees. Ann, Probab. 20 2089-2116.
    • (1992) Ann, Probab. , vol.20 , pp. 2089-2116
    • Pemantle, R.1
  • 76
    • 0000745699 scopus 로고
    • Field variants of barley yellow dwarf virus: Detection and fluctuation during twenty years
    • ROCHOW, W. F. (1979). Field variants of barley yellow dwarf virus: detection and fluctuation during twenty years. Phytopathology 69 655-660.
    • (1979) Phytopathology , vol.69 , pp. 655-660
    • Rochow, W.F.1
  • 77
    • 33645840905 scopus 로고
    • Non-equilibrium behaviour of a many particle process: Density profile and local equilibria
    • ROST, H. (1981). Non-equilibrium behaviour of a many particle process: density profile and local equilibria. Z. Wahrsch. Verw. Gebiete 58 41-53.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.58 , pp. 41-53
    • Rost, H.1
  • 79
    • 21344478294 scopus 로고
    • The asymmetric contact process on a finite set
    • SCHINAZI, R. (1994). The asymmetric contact process on a finite set. J. Statist. Phys. 74 1005-1016.
    • (1994) J. Statist. Phys. , vol.74 , pp. 1005-1016
    • Schinazi, R.1
  • 80
    • 0040729503 scopus 로고
    • Metastability for the contact process
    • SCHONMANN, R. H. (1985). Metastability for the contact process. J. Statist. Phys. 41 445-464.
    • (1985) J. Statist. Phys. , vol.41 , pp. 445-464
    • Schonmann, R.H.1
  • 81
    • 0040549871 scopus 로고
    • The asymmetric contact process
    • SCHONMANN, R. H. (1986). The asymmetric contact process. J. Statist. Phys. 44 505-534.
    • (1986) J. Statist. Phys. , vol.44 , pp. 505-534
    • Schonmann, R.H.1
  • 82
    • 0040540735 scopus 로고
    • A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter
    • SCHONMANN, R. H. (1987). A new proof of the complete convergence theorem for contact processes in several dimensions with large infection parameter. Ann. Probab. 15 382-387.
    • (1987) Ann. Probab. , vol.15 , pp. 382-387
    • Schonmann, R.H.1
  • 83
    • 21344478931 scopus 로고
    • Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region
    • SCHONMANN, R. H. (1994a). Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region. Comm. Math. Phys. 161 1-49.
    • (1994) Comm. Math. Phys. , vol.161 , pp. 1-49
    • Schonmann, R.H.1
  • 84
    • 0002244077 scopus 로고
    • Theorems and conjectures on the droplet-driven relaxation of Stochastic Ising models
    • G. Grimmett, ed. Kluwer, Dordrecht
    • SCHONMANN, R. H. (1994b). Theorems and conjectures on the droplet-driven relaxation of Stochastic Ising models. In Probability and Phase Transition (G. Grimmett, ed.) 265-301. Kluwer, Dordrecht.
    • (1994) Probability and Phase Transition , pp. 265-301
    • Schonmann, R.H.1
  • 85
    • 0039020026 scopus 로고
    • Metastability for the d-dimensional contact process
    • SIMONIS, A. (1991). Metastability for the d-dimensional contact process. J. Statist. Phys. 83 1225-1239.
    • (1991) J. Statist. Phys. , vol.83 , pp. 1225-1239
    • Simonis, A.1
  • 86
    • 0040261379 scopus 로고
    • Interaction of markov processes
    • SPITZER, F. (1970). Interaction of Markov processes. Adv. in Math. 5 246-290.
    • (1970) Adv. in Math. , vol.5 , pp. 246-290
    • Spitzer, F.1
  • 87
    • 0040771956 scopus 로고
    • Recurrent random walk of an infinite particle system
    • SPITZER, F. (1974). Recurrent random walk of an infinite particle system. Trans. Amer. Math. Soc. 198 191-199.
    • (1974) Trans. Amer. Math. Soc. , vol.198 , pp. 191-199
    • Spitzer, F.1
  • 90
    • 0030360082 scopus 로고    scopus 로고
    • The existence of an intermediate phase for the contact process on trees
    • STACEY, A. M. (1996). The existence of an intermediate phase for the contact process on trees. Ann. Probab. 24.
    • (1996) Ann. Probab. , vol.24
    • Stacey, A.M.1
  • 91
    • 0031065027 scopus 로고    scopus 로고
    • The asymmetric contact process at its second critical value
    • SWEET, T. (1997). The asymmetric contact process at its second critical value. J. Statist. Phys. 86.
    • (1997) J. Statist. Phys. , vol.86
    • Sweet, T.1
  • 94
    • 0002988718 scopus 로고
    • The contact process on a tree: Behavior near the first phase transition
    • WU, C. C. (1995). The contact process on a tree: behavior near the first phase transition. Stochastic Process. Appl. 57 99-112.
    • (1995) Stochastic Process. Appl. , vol.57 , pp. 99-112
    • Wu, C.C.1
  • 95
    • 0038993648 scopus 로고    scopus 로고
    • The complete convergence theorem of the contact process on trees
    • To appear
    • ZHANG, Y. (1997). The complete convergence theorem of the contact process on trees. Ann. Probab. 25. To appear.
    • (1997) Ann. Probab. , vol.25
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.