메뉴 건너뛰기




Volumn 99, Issue 3, 1999, Pages 419-453

Hölder regularity and dimension bounds for random curves

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001056718     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-09914-3     Document Type: Article
Times cited : (135)

References (41)
  • 1
    • 0031561930 scopus 로고    scopus 로고
    • On the number of incipient spanning clusters
    • M. Aizenman, On the number of incipient spanning clusters, Nuclear Phys. B 485 (1997), 551-582.
    • (1997) Nuclear Phys. B , vol.485 , pp. 551-582
    • Aizenman, M.1
  • 4
    • 0002217156 scopus 로고
    • Percolation and minimal spanning forests in infinite graphs
    • K. Alexander, Percolation and minimal spanning forests in infinite graphs, Ann. Probab. 23 (1995), 87-104.
    • (1995) Ann. Probab , vol.23 , pp. 87-104
    • Alexander, K.1
  • 5
    • 0030523782 scopus 로고    scopus 로고
    • The RSW theorem for continuum percolation and the CLT for Euclidean minimalspanning trees
    • K. Alexander, The RSW theorem for continuum percolation and the CLT for Euclidean minimal spanning trees, Ann. Appl. Probab. 6 (1996), 466-494.
    • (1996) Ann. Appl. Probab , vol.6 , pp. 466-494
    • Alexander, K.1
  • 6
    • 5844290410 scopus 로고
    • Self-organized criticality: An explanation of1 /f noise
    • P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of 1 /f noise, Phys. Rev. Lett. 59 (1987), 381-384.
    • (1987) Phys. Rev. Lett , vol.59 , pp. 381-384
    • Bak, P.1    Tang, C.2    Wiesenfeld, K.3
  • 8
    • 0032338824 scopus 로고    scopus 로고
    • Conformal invariance and Voronoipercolation
    • I. Benjamini and O. Schramm, Conformal invariance and Voronoipercolation, Comm. Math. Phys. 197 (1998), 75-107.
    • (1998) Comm. Math. Phys , vol.197 , pp. 75-107
    • Benjamini, I.1    Schramm, O.2
  • 10
    • 0031067246 scopus 로고    scopus 로고
    • The dimension of the Brownian frontier is greater than1
    • C. J. Bishop, P. W. Jones, R. Pemantle, and Y. Peres, The dimension of the Brownian frontier is greater than 1, J. Funct. Anal. 143 (1997), 309-336.
    • (1997) J. Funct. Anal , vol.143 , pp. 309-336
    • Bishop, C.J.1    Jones, P.W.2    Pemantle, R.3    Peres, Y.4
  • 12
    • 0000557204 scopus 로고
    • Nonintersection exponents for Brownian paths, II: Estimates and applications to a random fractal
    • K. Burdzy and G. Lawler, Nonintersection exponents for Brownian paths, II: Estimates and applications to a random fractal, Ann. Probab. 18 (1990), 981-1009.
    • (1990) Ann. Probab , vol.18 , pp. 981-1009
    • Burdzy, K.1    Lawler, G.2
  • 13
    • 0000898051 scopus 로고
    • Critical percolation in finite geometries
    • J. Cardy, Critical percolation in finite geometries, J. Phys. A 25 (1992), L201-L206.
    • (1992) J. Phys. A , vol.25 , pp. L201-L206
    • Cardy, J.1
  • 15
    • 0004919658 scopus 로고
    • The stochastic geometry of invasion percolation
    • J. Chayes, L. Chayes, and C. M. Newman, The stochastic geometry of invasion percolation, Comm. Math. Phys. 101 (1985), 383-407.
    • (1985) Comm. Math. Phys , vol.101 , pp. 383-407
    • Chayes, J.1    Chayes, L.2    Newman, C.M.3
  • 16
    • 0001813888 scopus 로고
    • An invariance principle for certain probability limit theorems
    • M. Donsker, An invariance principle for certain probability limit theorems, Mem. Amer. Math. Soc. 1951, no. 6.
    • (1951) Mem. Amer. Math. Soc , Issue.6
    • Donsker, M.1
  • 17
    • 38249011042 scopus 로고
    • The divider dimension of the graph of a function
    • S. Dunbar, R. Douglass, and W. Camp, The divider dimension of the graph of a function, J. Math. Anal. Appl. 167 (1992), 403-413.
    • (1992) J.Math. Anal. Appl , vol.167 , pp. 403-413
    • Dunbar, S.1    Douglass, R.2    Camp, W.3
  • 18
    • 0039098476 scopus 로고
    • Note on the transfinite diameter
    • P. Erdős and J. Gillis, Note on the transfinite diameter, J. London Math. Soc. 12 (1937), 185-192.
    • (1937) J. London Math. Soc , vol.12 , pp. 185-192
    • Erd, P.1    Ősgillis, J.2
  • 19
    • 0003358442 scopus 로고
    • The Geometry of Fractal Sets
    • Cambridge Univ. Press, Cambridge
    • K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Math. 85, Cambridge Univ. Press, Cambridge, 1985.
    • (1985) Cambridge Tracts in Math , vol.85
    • Falconer, K.J.1
  • 20
    • 0000109109 scopus 로고
    • The configuration of real polymer chains
    • P. Flory, The configuration of real polymer chains, J. Chem. Phys. 17 (1949), 303-310.
    • (1949) J. Chem. Phys , vol.17 , pp. 303-310
    • Flory, P.1
  • 21
    • 0004246476 scopus 로고
    • Springer-Verlag, New York
    • G. Grimmett, Percolation, Springer-Verlag, New York, 1989.
    • (1989) Percolation
    • Grimmett, G.1
  • 22
    • 0002225510 scopus 로고
    • Random-cluster measures and uniform spanning trees
    • O. Häggström, Random-cluster measures and uniform spanning trees, Stochastic Process Appl. 59 (1995), 267-275.
    • (1995) Stochastic Process Appl , vol.59 , pp. 267-275
    • Häggström, O.1
  • 23
    • 0001755621 scopus 로고
    • Scaling relations for 2D-percolation
    • H. Kesten, Scaling relations for 2D-percolation, Comm. Math. Phys. 109 (1987), 109-156.
    • (1987) Comm. Math. Phys , vol.109 , pp. 109-156
    • Kesten, H.1
  • 24
    • 21144469806 scopus 로고
    • The tortuosity of occupied crossings of a box in critical percolation
    • H. Kesten and Y. Zhang, The tortuosity of occupied crossings of a box in critical percolation, J. Statist. Phys. 70 (1993), 599-611.
    • (1993) J. Statist. Phys , vol.70 , pp. 599-611
    • Kesten, H.1    Zhang, Y.2
  • 25
    • 0000886019 scopus 로고
    • Geometrical exponents of contour loops on random Gaussian surfaces
    • J. Kondev and C. Henley, Geometrical exponents of contour loops on random Gaussian surfaces, Phys. Rev. Lett. 74 (1995), 4580-4583.
    • (1995) Phys. Rev. Lett , vol.74 , pp. 4580-4583
    • Kondev, J.1    Henley, C.2
  • 27
    • 0003257551 scopus 로고    scopus 로고
    • The dimension of the frontier of planar Brownian motion
    • paper 5, electronic
    • G. Lawler, The dimension of the frontier of planar Brownian motion, Electron. Comm. Probab. 1 (1996), paper 5, 29-47 (electronic).
    • (1996) Electron. Comm. Probab , vol.1 , pp. 29-47
    • Lawler, G.1
  • 28
    • 3042574952 scopus 로고    scopus 로고
    • Hausdorff dimension of cut points for Brownian motion
    • paper 2, electronic
    • G. Lawler, Hausdorff dimension of cut points for Brownian motion, Electron. J. Probab. 1 (1996) paper 2, 20 pp. (electronic).
    • (1996) Electron. J. Probab , vol.1 , pp. 20
    • Lawler, G.1
  • 30
    • 4243770159 scopus 로고
    • Spin-glass model with dimension-dependent ground statemultiplicity
    • C. M. Newman and D. L. Stein, Spin-glass model with dimension-dependent ground state multiplicity, Phys. Rev. Lett. 72 (1994), 2286-2289.
    • (1994) Phys. Rev. Lett , vol.72 , pp. 2286-2289
    • Newman, C.M.1    Stein, D.L.2
  • 31
    • 0001356366 scopus 로고    scopus 로고
    • Ground-state structure in a highly disordered spin-glass model
    • C. M. Newman and D. L. Stein, Ground-state structure in a highly disordered spin-glass model, J. Statist. Phys. 82 (1996), 1113-1132.
    • (1996) J. Statist. Phys , vol.82 , pp. 1113-1132
    • Newman, C.M.1    Stein, D.L.2
  • 32
    • 0000000702 scopus 로고
    • Choosing a spanning tree for the integer lattice uniformly
    • R. Pemantle, Choosing a spanning tree for the integer lattice uniformly, Ann. Probab. 19 (1991), 1559-1574.
    • (1991) Ann. Probab , vol.19 , pp. 1559-1574
    • Pemantle, R.1
  • 33
    • 0000033355 scopus 로고
    • Convergence of random processes and limit theorems in probability theory
    • Y. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl. 1 (1956), 157-214.
    • (1956) Theory Probab. Appl , vol.1 , pp. 157-214
    • Prokhorov, Y.V.1
  • 34
    • 0001650381 scopus 로고
    • The problem of contiguity
    • Society for the Advancement of General Systems Theory, Ann Arbor, Mich
    • L. Richardson, “The problem of contiguity” in General Systems: Yearbook 6, Society for the Advancement of General Systems Theory, Ann Arbor, Mich., 1961, 139-187.
    • (1961) General Systems: Yearbook , vol.6 , pp. 139-187
    • Richardson, L.1
  • 35
    • 34250275869 scopus 로고
    • A note on percolation, Z. Wahrscheinlichkeitstheorie und Verw
    • L. Russo, A note on percolation, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 43 (1978), 39-48.
    • (1978) Gebiete , vol.43 , pp. 39-48
    • Russo, L.1
  • 36
    • 0001193785 scopus 로고
    • Exact determination of the percolation hull exponent in twodimensions
    • H. Saleur and B. Duplantier, Exact determination of the percolation hull exponent in two dimensions, Phys. Rev. Lett. 58 (1987), 2325-2328.
    • (1987) Phys. Rev. Lett , vol.58 , pp. 2325-2328
    • Saleur, H.1    Duplantier, B.2
  • 37
    • 77957093986 scopus 로고
    • Percolation probabilities on the square lattice
    • North-Holland, Amsterdam
    • P. Seymour and D. Welsh, “Percolation probabilities on the square lattice” in Advances in Graph Theory, Ann. Discrete Math. 3, North-Holland, Amsterdam, 1978, 227-245.
    • (1978) Advances in Graph Theory, Ann. Discrete Math , vol.3 , pp. 227-245
    • Seymour, P.1    Welsh, D.2
  • 38
    • 30544439717 scopus 로고
    • Cluster shapes at the percolation threshold: An effective cluster dimensionality and its connection with critical-point exponents
    • H. E. Stanley, Cluster shapes at the percolation threshold: An effective cluster dimensionality and its connection with critical-point exponents, J. Phys. A 10 (1977), L211- L220.
    • (1977) J. Phys. A , vol.10
    • Stanley, H.E.1
  • 40
    • 0022116584 scopus 로고
    • Inequalities with applications to percolation and reliability
    • J. van den Berg and H. Kesten, Inequalities with applications to percolation and reliability, J. Appl. Probab. 22 (1985), 556-569.
    • (1985) J. Appl. Probab , vol.22 , pp. 556-569
    • Van Den Berg, J.1    Kesten, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.