메뉴 건너뛰기




Volumn 5, Issue 1, 2008, Pages 1-36

Existence and spatial limit theorems for lattice and continuum particle systems

Author keywords

Functional central limit theorem; Interacting particle system; Point process

Indexed keywords


EID: 77949290218     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/07-PS112     Document Type: Article
Times cited : (40)

References (63)
  • 1
    • 0000669932 scopus 로고
    • Invariant measures for the zero range processes
    • MR0659526
    • Andjel, E. D. (1982) Invariant measures for the zero range processes. Ann. Probab. 10, 525-547. MR0659526
    • (1982) Ann. Probab. , vol.10 , pp. 525-547
    • Andjel, E.D.1
  • 2
    • 3042653741 scopus 로고    scopus 로고
    • Ballistic deposition on a planar strip
    • MR1826165
    • R. Atar, S. Athreya and M. Kang (2001) Ballistic deposition on a planar strip. Elec. Comm. Probab. 6, 31-38. MR1826165
    • (2001) Elec. Comm. Probab. , vol.6 , pp. 31-38
    • Atar, R.1    Athreya, S.2    Kang, M.3
  • 3
    • 0002826444 scopus 로고
    • Nearest-Neighbour Markov Point processes and random sets
    • Baddeley, A. and Møller, J. (1989) Nearest-Neighbour Markov Point processes and random sets. Internat. Statist. Rev. 57, 89-121.
    • (1989) Internat. Statist. Rev. , vol.57 , pp. 89-121
    • Baddeley, A.1    Møller, J.2
  • 4
    • 51549092213 scopus 로고    scopus 로고
    • Existence of the zero range process and a deposition model with superlinear growth rates
    • MR2330972
    • Baĺazs, M., Rassoul-Agha, F., Sepp̈al̈ainen, T. and Sethuraman, S. (2007) Existence of the zero range process and a deposition model with superlinear growth rates. Ann. Probab. 35 1201-1249. MR2330972
    • (2007) Ann. Probab. , vol.35 , pp. 1201-1249
    • Baĺazs, M.1    Rassoul-Agha, F.2    Sepp̈al̈ainen, T.3    Sethuraman, S.4
  • 6
    • 0037279607 scopus 로고    scopus 로고
    • Gaussian fields and random packing
    • MR1964280
    • Baryshnikov, Y and Yukich, J. E. Gaussian fields and random packing. J. Stat. Physics, 111, 443-463. MR1964280
    • J. Stat. Physics , vol.111 , pp. 443-463
    • Baryshnikov, Y.1    Yukich, J.E.2
  • 7
    • 33748129931 scopus 로고    scopus 로고
    • Infinite-dimensional Markov processes with almost local interaction of the components
    • MR0426218
    • Basis, V. Ya. Infinite-dimensional Markov processes with almost local interaction of the components. Theory Probab. Appl. 21, 706-720. MR0426218
    • Theory Probab. Appl. , vol.21 , pp. 706-720
    • Basis, V.Y.1
  • 8
    • 33748208201 scopus 로고
    • Stationarity and ergodicity of Markov interacting processes Multicomponent random systems
    • Related Topics 6 Dekker, New York, 1980. MR0599532
    • Basis, V. Ya. (1980) Stationarity and ergodicity of Markov interacting processes. Multicomponent random systems, pp. 37-58, Adv. Probab. Related Topics 6 Dekker, New York, 1980. MR0599532
    • (1980) Adv. Probab. , pp. 37-58
    • Basis, V.Y.1
  • 9
    • 0010333409 scopus 로고
    • A geometrical approach to the structure of liquids
    • J. D. Bernal (1959) A geometrical approach to the structure of liquids. Nature, 183 141-147.
    • (1959) Nature , vol.183 , pp. 141-147
    • Bernal, J.D.1
  • 10
    • 33845544986 scopus 로고
    • Co-ordination of randomly packed spheres
    • J. D. Bernal and J. Mason (1960) Co-ordination of randomly packed spheres. Nature, 188, 910-911.
    • (1960) Nature , vol.188 , pp. 910-911
    • Bernal, J.D.1    Mason, J.2
  • 13
    • 0000764301 scopus 로고
    • First-layer formation in ballistic deposition of spherical particles: Kinetics and structure
    • H. S. Choi, J. Talbot, G. Tarjus and P. Viot (1993) First-layer formation in ballistic deposition of spherical particles: Kinetics and structure. J. Chem. Phys. 99, 9296-9303.
    • (1993) J. Chem. Phys. , vol.99 , pp. 9296-9303
    • Choi, H.S.1    Talbot, J.2    Tarjus, G.3    Viot, P.4
  • 17
    • 9744251040 scopus 로고    scopus 로고
    • The Abelian sandpiles and related models
    • Dhar, D. (1999) The Abelian sandpiles and related models. Phys. A 263, 4-25.
    • (1999) Phys. A , vol.263 , pp. 4-25
    • Dhar, D.1
  • 18
    • 84890635837 scopus 로고    scopus 로고
    • A functional central limit theorem for interacting particle systems on transitive graphs
    • to appear. Preprint available at ArXiv.mathph/ 0509041.
    • Doukhan, P., Lang, G., Louhichi, S. and Ycart, B. (2005). A functional central limit theorem for interacting particle systems on transitive graphs. Markov Proc. Rel. Fields, to appear. Preprint available at ArXiv.mathph/ 0509041.
    • (2005) Markov Proc. Rel. Fields
    • Doukhan, P.1    Lang, G.2    Louhichi, S.3    Ycart, B.4
  • 21
    • 12044256185 scopus 로고
    • Random and cooperative adsorption
    • J. W. Evans (1993) Random and cooperative adsorption. Rev. Modern Phys. 65, 1281-1329.
    • (1993) Rev. Modern Phys. , vol.65 , pp. 1281-1329
    • Evans, J.W.1
  • 23
    • 0036830424 scopus 로고    scopus 로고
    • Perfect simulation for interacting point processes, loss networks and Ising models.
    • MR1934155
    • Ferrari, P. A., Ferńandez, R., and Garcia, N. L. (2002) Perfect simulation for interacting point processes, loss networks and Ising models. Stoch. Process. Applns. 102, 63-88. MR1934155
    • (2002) Stoch. Process. Applns. , vol.102 , pp. 63-88
    • Ferrari, P.A.1    Ferńandez, R.2    Garcia, N.L.3
  • 25
    • 44149099843 scopus 로고    scopus 로고
    • Spatial birth and death processes as solutions of stochastic equations.
    • MR2249658
    • Garcia, N. L. and Kurtz, T. G. (2006) Spatial birth and death processes as solutions of stochastic equations. Alea 1, 288-303. MR2249658
    • (2006) Alea , vol.1 , pp. 288-303
    • Garcia, N.L.1    Kurtz, T.G.2
  • 26
    • 0011653726 scopus 로고
    • Time-reversible and Gibbsian point processes I Markovian and spatial birth and death processes on a general phase
    • MR0642153
    • Gl̈otzl, E. (1981). Time-reversible and Gibbsian point processes I. Markovian and spatial birth and death processes on a general phase space. Math. Nachr. 102, 217-222. MR0642153
    • (1981) space. Math. Nachr , vol.102 , pp. 217-222
    • Gl̈otzl, E.1
  • 27
    • 34250220198 scopus 로고
    • Time-reversible and Gibbsian point processes II. Markovian particle jump processes on a general phase space
    • MR0675745
    • Gl̈otzl, E. (1982). Time-reversible and Gibbsian point processes II. Markovian particle jump processes on a general phase space. Math. Nachr. 106, 63-71. MR0675745
    • (1982) Math. Nachr. , vol.106 , pp. 63-71
    • Gl̈otzl, E.1
  • 28
    • 0003239547 scopus 로고
    • Additive and Cancellative Interacting Particle Systems
    • Springer, Berlin. MR0538077
    • Griffeath, D. (1979). Additive and Cancellative Interacting Particle Systems. Lecture notes in Math. 724, Springer, Berlin. MR0538077
    • (1979) Lecture notes in Math. , vol.724
    • Griffeath, D.1
  • 29
    • 0040732064 scopus 로고
    • Coordination number of disordered packings of identical spheres
    • MR1004917
    • A. Gervois, M. Lichtenberg, L. Oger, and E. Guyon (1989) Coordination number of disordered packings of identical spheres. J. Phys. A: Math, Gen. 22 2119-2131. MR1004917
    • (1989) J. Phys. A: Math, Gen. , vol.22 , pp. 2119-2131
    • Gervois, A.1    Lichtenberg, M.2    Oger, L.3    Guyon, E.4
  • 30
    • 0000387510 scopus 로고
    • Statistical geometrical approach to random packing density of equal spheres
    • K. Gotoh and J. L. Finney (1974) Statistical geometrical approach to random packing density of equal spheres. Nature, 252, 202-205.
    • (1974) Nature , vol.252 , pp. 202-205
    • Gotoh, K.1    Finney, J.L.2
  • 31
    • 0002107841 scopus 로고
    • Nearest-neighbor Markov interaction processes on multidimensional lattices
    • MR0307392
    • Harris, T. E. (1972). Nearest-neighbor Markov interaction processes on multidimensional lattices. Adv. Math. 9, 66-89. MR0307392
    • (1972) Adv. Math. , vol.9 , pp. 66-89
    • Harris, T.E.1
  • 32
    • 0343044647 scopus 로고
    • Markovian interaction processes with finite range interactions
    • MR0373070
    • Holley, R. (1972) Markovian interaction processes with finite range interactions. Ann. Math. Stat. 43, 1961-1967. MR0373070
    • (1972) Ann. Math. Stat. , vol.43 , pp. 1961-1967
    • Holley, R.1
  • 33
    • 2942645862 scopus 로고
    • Nearest neighbour birth and death processes on the real line
    • MR0488380
    • Holley, R. and Stroock, D. W. (1978) Nearest neighbour birth and death processes on the real line. Acta Math. 140, 103-154. MR0488380
    • (1978) Acta Math , vol.140 , pp. 103-154
    • Holley, R.1    Stroock, D.W.2
  • 34
    • 0010779935 scopus 로고
    • Central limit phenomena of various interacting systems
    • MR0549491
    • Holley, R. ad Stroock, D. W. (1979) Central limit phenomena of various interacting systems. Ann. Math. 110, 333-393. MR0549491
    • (1979) Ann. Math. , vol.110 , pp. 333-393
    • Holley, R.1    Stroock, D.W.2
  • 35
    • 49349096300 scopus 로고    scopus 로고
    • Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes
    • MR2189574
    • Jacobsen, M. (2006) Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes. Birkḧauser. MR2189574
    • (2006) Birkḧauser
    • Jacobsen, M.1
  • 36
    • 22944443017 scopus 로고
    • Computer simulation of close random packing of equal spheres
    • W. S. Jodrey and E. M. Torey (1985) Computer simulation of close random packing of equal spheres. Phys. Review A, 32, 2347-2351.
    • (1985) Phys. Review A , vol.32 , pp. 2347-2351
    • Jodrey, W.S.1    Torey, E.M.2
  • 37
    • 0023530964 scopus 로고
    • Simple three-dimensional models for ballistic deposition and restructuring
    • R. Jullien and P. Meakin (1987) Simple three-dimensional models for ballistic deposition and restructuring. Europhys. Lett. 4, 1385-1390.
    • (1987) Europhys. Lett. , vol.4 , pp. 1385-1390
    • Jullien, R.1    Meakin, P.2
  • 39
    • 84966222217 scopus 로고
    • Existence theorems for infinite particle systems
    • MR0309218
    • Liggett, T. M. (1972) Existence theorems for infinite particle systems. Transactions Amer. Math. Soc. 165, 471-481. MR0309218
    • (1972) Transactions Amer. Math. Soc. , vol.165 , pp. 471-481
    • Liggett, T.M.1
  • 41
    • 0001736104 scopus 로고
    • Ergodic theorems for coupled random walks and other systems with locally interacting components
    • MR0621659
    • Liggett, T. M. and Spitzer, F. (1981) Ergodic theorems for coupled random walks and other systems with locally interacting components. Z. Wahrsch. Verw. Gebiete 56 443-468. MR0621659
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , pp. 443-468
    • Liggett, T.M.1    Spitzer, F.2
  • 42
    • 0036821635 scopus 로고    scopus 로고
    • The abelian sandpile model on an infinite tree
    • MR1944016
    • Maes, C. M., Redig, F. and Saada, E. (2002) The abelian sandpile model on an infinite tree. Ann. Probab. 30, 2081-2107. MR1944016
    • (2002) Ann. Probab. , vol.30 , pp. 2081-2107
    • Maes, C.M.1    Redig, F.2    Saada, E.3
  • 44
    • 0001655886 scopus 로고
    • Randomloose packings of uniformspheres and the dilatancy onset
    • Onoda, G. and Liniger, E. (1990) Randomloose packings of uniformspheres and the dilatancy onset. Phys. Rev. Letters, 64, 2727-2730.
    • (1990) Phys. Rev. Letters , vol.64 , pp. 2727-2730
    • Onoda, G.1    Liniger, E.2
  • 45
    • 0035531727 scopus 로고    scopus 로고
    • Random parking, sequential adsorption, and the jamming limit
    • MR1824203
    • Penrose, M. D. (2001) Random parking, sequential adsorption, and the jamming limit. Comm. Math. Phys. 218, 153-176. MR1824203
    • (2001) Comm. Math. Phys. , vol.218 , pp. 153-176
    • Penrose, M.D.1
  • 46
    • 0035498178 scopus 로고    scopus 로고
    • Limit theory for monolayer ballistic deposition in the continuum
    • MR1871657
    • Penrose, M. D. (2001) Limit theory for monolayer ballistic deposition in the continuum. J. Statist. Phys. 105, 561-583. MR1871657
    • (2001) J. Statist. Phys. , vol.105 , pp. 561-583
    • Penrose, M.D.1
  • 47
    • 0036189628 scopus 로고    scopus 로고
    • Limit theory for monotonic particle systems and sequential deposition
    • MR1887532
    • Penrose, M. D. (2002) Limit theory for monotonic particle systems and sequential deposition. Stoch. Proc. Appln. 98 175-197. MR1887532
    • (2002) Stoch. Proc. Appln. , vol.98 , pp. 175-197
    • Penrose, M.D.1
  • 48
    • 27644525072 scopus 로고    scopus 로고
    • Multivariate spatial central limit theorems with applications to percolation and spatial graphs
    • MR2165584
    • Penrose, M. D. (2005) Multivariate spatial central limit theorems with applications to percolation and spatial graphs. Ann. Probab. 33, 1945-1991. MR2165584
    • (2005) Ann. Probab. , vol.33 , pp. 1945-1991
    • Penrose, M.D.1
  • 49
    • 14544306529 scopus 로고    scopus 로고
    • Exact and approximate results for deposition and annihilation processes on graphs
    • MR2114992
    • Penrose, M.D. and Sudbury, A. (2005) Exact and approximate results for deposition and annihilation processes on graphs. Ann. Appl. Probab. 15, 853-889 (2005). MR2114992
    • (2005) Ann. Appl. Probab. , vol.15 , Issue.2005 , pp. 853-889
    • Penrose, M.D.1    Sudbury, A.2
  • 50
    • 0036117358 scopus 로고    scopus 로고
    • Limit theory for random sequential packing and deposition
    • MR1890065
    • Penrose, M. D. and Yukich, J. E. (2002) Limit theory for random sequential packing and deposition. Ann. Appl. Probab. 12, 232-301. MR1890065
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 232-301
    • Penrose, M.D.1    Yukich, J.E.2
  • 51
    • 0035903075 scopus 로고    scopus 로고
    • Mathematics of random growing interfaces
    • MR1862710
    • Penrose, M. D. and Yukich, J. E. (2001) Mathematics of random growing interfaces. J. Phys. A: Math. Gen. 34, 6239-6247. MR1862710
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 6239-6247
    • Penrose, M.D.1    Yukich, J.E.2
  • 52
    • 0001699493 scopus 로고
    • Spatial birth-and-death processes
    • MR0474532
    • Preston, C. J. (1975) Spatial birth-and-death processes. Bull. Int. Statist. Inst. 46 (2) 371-391. MR0474532
    • (1975) Bull. Int. Statist. Inst. , vol.46 , Issue.2 , pp. 371-391
    • Preston, C.J.1
  • 55
    • 35148867317 scopus 로고
    • Packing of spheres
    • Scott, G. D. (1960) Packing of spheres. Nature, 188, 908-909.
    • (1960) Nature , vol.188 , pp. 908-909
    • Scott, G.D.1
  • 56
    • 0033971435 scopus 로고    scopus 로고
    • Irreversible adsorption of colloidal particles on solid substrates
    • B. Senger, J.-C. Voegel, P. Schaaf (2000) Irreversible adsorption of colloidal particles on solid substrates. Colloids and Surfaces A 165, 255-285.
    • (2000) Colloids and Surfaces A , vol.165 , pp. 255-285
    • Senger, B.1    Voegel, J.-C.2    Schaaf, P.3
  • 57
    • 0034368725 scopus 로고    scopus 로고
    • Strong law of large numbers for the interface in ballistic deposition
    • MR1797390
    • Sepp̈al̈ainen, T. (2000) Strong law of large numbers for the interface in ballistic deposition. Ann. Inst. H. Poincaŕe Probab. Statist. 36, 691-736. MR1797390
    • (2000) Ann. Inst. H. Poincaŕe Probab. Statist. , vol.36 , pp. 691-736
    • Sepp̈al̈ainen, T.1
  • 58
    • 58149365464 scopus 로고
    • Ergodicity of Spitzer's renewal model
    • MR1312152
    • Sidoravícius, V. and Vares, M. E. (1995) Ergodicity of Spitzer's renewal model. Stochastic Process. Appl. 55 119-130. MR1312152
    • (1995) Stochastic Process. Appl. , vol.55 , pp. 119-130
    • Sidoravícius, V.1    Vares, M.E.2
  • 59
    • 0007067868 scopus 로고
    • Random Packing Density
    • Univ. California Press. MR0256531
    • H. Solomon (1967) Random Packing Density. Proc. Fifth Berkeley Symp. on Prob. and Stat. 3, 119-134, Univ. California Press. MR0256531
    • (1967) Proc. Fifth Berkeley Symp. on Prob. and Stat. , vol.3 , pp. 119-134
    • Solomon, H.1
  • 61
  • 62
    • 0004228766 scopus 로고
    • Cambridge University Press, Cambridge. MR1155402
    • Williams, D. (1991) Probability with Martingales. Cambridge University Press, Cambridge. MR1155402
    • (1991) Probability with Martingales
    • Williams, D.1
  • 63
    • 0004025266 scopus 로고    scopus 로고
    • Springer, New York. MR1707318
    • Zong, C. (1999) Sphere Packings. Springer, New York. MR1707318
    • (1999) Sphere Packings
    • Zong, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.