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Volumn 50, Issue 1, 2006, Pages 33-65

Random Walk on The Incipient Infinite Cluster on Trees

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EID: 33846275876     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1258059469     Document Type: Article
Times cited : (80)

References (39)
  • 1
    • 0001981461 scopus 로고
    • The continuum random tree. I
    • MR 1085326 91i:60024
    • D. Aldous, The continuum random tree. I, Ann. Probab. 19 (1991), 1-28. MR 1085326 (91i:60024)
    • (1991) Ann. Probab , vol.19 , pp. 1-28
    • Aldous, D.1
  • 2
    • 0001812090 scopus 로고
    • The continuum random tree. II. An overview
    • Stochastic analysis (Durham, London Math. Soc, Cambridge Univ. Press, Cambridge, MR 1166406 93f:60010
    • _, The continuum random tree. II. An overview, Stochastic analysis (Durham, 1990), London Math. Soc. Lecture Note Ser., vol. 167, Cambridge Univ. Press, Cambridge, 1991, pp. 23-70. MR 1166406 (93f:60010)
    • (1990) Lecture Note Ser , vol.167 , pp. 23-70
    • Aldous, D.1
  • 3
    • 0003296611 scopus 로고
    • The continuum random tree. III
    • MR 1207226 94c:60015
    • _, The continuum random tree. III, Ann. Probab. 21 (1993), 248-289. MR 1207226 (94c:60015)
    • (1993) Ann. Probab , vol.21 , pp. 248-289
    • Aldous, D.1
  • 4
    • 0020186194 scopus 로고
    • Density of states on fractals: "fractons", J
    • S. Alexander and R. Orbach, Density of states on fractals: "fractons", J. Physique (Paris) Lett. 43 (1982), L625-L631.
    • (1982) Physique (Paris) Lett , vol.43
    • Alexander, S.1    Orbach, R.2
  • 5
    • 33846266170 scopus 로고    scopus 로고
    • M. T. Barlow, Diffusions on fractals, Lectures on probability theory and statistics (Saint-Flour, 1995), Lecture Notes in Math., 1690, Springer, Berlin, 1998, pp. 1-121. MR 1668115 (2000a:60148)
    • M. T. Barlow, Diffusions on fractals, Lectures on probability theory and statistics (Saint-Flour, 1995), Lecture Notes in Math., vol. 1690, Springer, Berlin, 1998, pp. 1-121. MR 1668115 (2000a:60148)
  • 6
    • 4243129698 scopus 로고    scopus 로고
    • _, Random walks on supercritical percolation clusters, Ann. Probab. 32 (2004), 3024-3084. MR 2094438 (2006e:60146)
    • _, Random walks on supercritical percolation clusters, Ann. Probab. 32 (2004), 3024-3084. MR 2094438 (2006e:60146)
  • 7
    • 0001035130 scopus 로고
    • The construction of Brownian motion on the Sierpiński carpet
    • MR 1023950 91d:60183
    • M. T. Barlow and R. F. Bass, The construction of Brownian motion on the Sierpiński carpet, Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), 225-257. MR 1023950 (91d:60183)
    • (1989) Ann. Inst. H. Poincaré Probab. Statist , vol.25 , pp. 225-257
    • Barlow, M.T.1    Bass, R.F.2
  • 8
    • 33846306307 scopus 로고    scopus 로고
    • _, Random walks on graphical Sierpinski carpets, Random walks and discrete potential theory (Cortona, 1997), Sympos. Math., XXXIX, Cambridge Univ. Press, Cambridge, 1999, pp. 26-55. MR 1802425 (2002c:60116)
    • _, Random walks on graphical Sierpinski carpets, Random walks and discrete potential theory (Cortona, 1997), Sympos. Math., XXXIX, Cambridge Univ. Press, Cambridge, 1999, pp. 26-55. MR 1802425 (2002c:60116)
  • 9
    • 29344454807 scopus 로고    scopus 로고
    • Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs
    • MR 2177164
    • M. T. Barlow, T. Coulhon, and T. Kumagai, Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs, Comm. Pure Appl. Math. 58 (2005), 1642-1677. MR 2177164
    • (2005) Comm. Pure Appl. Math , vol.58 , pp. 1642-1677
    • Barlow, M.T.1    Coulhon, T.2    Kumagai, T.3
  • 12
    • 0035539932 scopus 로고    scopus 로고
    • C. Borgs, J. T. Chayes, H. Kesten, and J. Spencer, The birth of the infinite cluster: finite-size scaling in percolation, Comm. Math. Phys. 224 (2001), 153-204. MR 1868996 (2002k:60199)
    • C. Borgs, J. T. Chayes, H. Kesten, and J. Spencer, The birth of the infinite cluster: finite-size scaling in percolation, Comm. Math. Phys. 224 (2001), 153-204. MR 1868996 (2002k:60199)
  • 15
    • 0000441817 scopus 로고
    • Super-Brownian motion: Path properties and hitting probabilities
    • MR 1012498 90k:60073
    • D. A. Dawson, I. Iscoe, and E. A. Perkins, Super-Brownian motion: path properties and hitting probabilities, Probab. Theory Related Fields 83 (1989), 135-205. MR 1012498 (90k:60073)
    • (1989) Probab. Theory Related Fields , vol.83 , pp. 135-205
    • Dawson, D.A.1    Iscoe, I.2    Perkins, E.A.3
  • 16
    • 0001131105 scopus 로고
    • An invariance principle for reversible Markov processes. Applications to random motions in random environments
    • MR 1003538 91e:60107
    • A. De Masi, P. A. Ferrari, S. Goldstein, and W. D. Wick, An invariance principle for reversible Markov processes. Applications to random motions in random environments, J. Statist. Phys. 55 (1989), 787-855. MR 1003538 (91e:60107)
    • (1989) J. Statist. Phys , vol.55 , pp. 787-855
    • De Masi, A.1    Ferrari, P.A.2    Goldstein, S.3    Wick, W.D.4
  • 17
    • 0002384441 scopus 로고
    • On tail probabilities for martingales
    • MR 0380971 52 #1868
    • D. A. Freedman, On tail probabilities for martingales, Ann. Probability 3 (1975), 100-118. MR 0380971 (52 #1868)
    • (1975) Ann. Probability , vol.3 , pp. 100-118
    • Freedman, D.A.1
  • 18
    • 0000763788 scopus 로고    scopus 로고
    • A. Grigoryan and A. Telcs, Sub-Gaussian estimates of heat kernels on infinite graphs, Duke Math. J. 109 (2001), 451-510. MR 1853353 (2003a:35085)
    • A. Grigoryan and A. Telcs, Sub-Gaussian estimates of heat kernels on infinite graphs, Duke Math. J. 109 (2001), 451-510. MR 1853353 (2003a:35085)
  • 19
    • 0036981648 scopus 로고    scopus 로고
    • _, Harnack inequalities and sub-Gaussian estimates for random walks, Math. Ann. 324 (2002), 521-556. MR 1938457 (2003i:58068)
    • _, Harnack inequalities and sub-Gaussian estimates for random walks, Math. Ann. 324 (2002), 521-556. MR 1938457 (2003i:58068)
  • 21
    • 33846325807 scopus 로고    scopus 로고
    • B. M. Hambly and T. Kumagai, Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries, Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, Proc. Sympos. Pure Math., 72, Amer. Math. Soc., Providence, RI, 2004, pp. 233-259. MR 2112125 (2005k:60141)
    • B. M. Hambly and T. Kumagai, Heat kernel estimates for symmetric random walks on a class of fractal graphs and stability under rough isometries, Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, Proc. Sympos. Pure Math., vol. 72, Amer. Math. Soc., Providence, RI, 2004, pp. 233-259. MR 2112125 (2005k:60141)
  • 22
    • 34249952953 scopus 로고
    • Mean-field critical behaviour for percolation in high dimensions
    • MR 1043524 91a:82037
    • T. Hara and G. Slade, Mean-field critical behaviour for percolation in high dimensions, Comm. Math. Phys. 128 (1990), 333-391. MR 1043524 (91a:82037)
    • (1990) Comm. Math. Phys , vol.128 , pp. 333-391
    • Hara, T.1    Slade, G.2
  • 23
    • 0004010598 scopus 로고
    • Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin, MR 0163361 29 #664
    • T. E. Harris, The theory of branching processes, Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin, 1963. MR 0163361 (29 #664)
    • (1963) The theory of branching processes
    • Harris, T.E.1
  • 25
    • 0036882738 scopus 로고    scopus 로고
    • R. van der Hofstad, F. den Hollander, and G. Slade, Construction of the incipient infinite cluster for spread-out oriented percolation above 4 + 1 dimensions, Comm. Math. Phys. 231 (2002), 435-461. MR 1946445 (2003j:60141)
    • R. van der Hofstad, F. den Hollander, and G. Slade, Construction of the incipient infinite cluster for spread-out oriented percolation above 4 + 1 dimensions, Comm. Math. Phys. 231 (2002), 435-461. MR 1946445 (2003j:60141)
  • 26
    • 3543047374 scopus 로고    scopus 로고
    • R. van der Hofstad and A. A. Járai, The incipient infinite cluster for high-dimensional unoriented percolation, J. Statist. Phys. 114 (2004), 625-663. MR 2035627 (2004m:82059)
    • R. van der Hofstad and A. A. Járai, The incipient infinite cluster for high-dimensional unoriented percolation, J. Statist. Phys. 114 (2004), 625-663. MR 2035627 (2004m:82059)
  • 27
    • 0037402965 scopus 로고    scopus 로고
    • R. van der Hofstad and G. Slade, Convergence of critical oriented percolation to super-Brownian motion above 4 + 1 dimensions, Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), 413-485. MR 1978987 (2004a:60158)
    • R. van der Hofstad and G. Slade, Convergence of critical oriented percolation to super-Brownian motion above 4 + 1 dimensions, Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), 413-485. MR 1978987 (2004a:60158)
  • 28
    • 0037248415 scopus 로고    scopus 로고
    • A. A. Járai, Incipient infinite percolation clusters in 2D, Ann. Probab. 31 (2003), 444-485. MR 1959799 (2004a:60159)
    • A. A. Járai, Incipient infinite percolation clusters in 2D, Ann. Probab. 31 (2003), 444-485. MR 1959799 (2004a:60159)
  • 29
    • 17344376584 scopus 로고    scopus 로고
    • _, Invasion percolation and the incipient infinite cluster in 2D, Comm. Math. Phys. 236 (2003), 311-334. MR 1981994 (2004c:82111)
    • _, Invasion percolation and the incipient infinite cluster in 2D, Comm. Math. Phys. 236 (2003), 311-334. MR 1981994 (2004c:82111)
  • 30
    • 0029690374 scopus 로고    scopus 로고
    • Transition probabilities for the simple random walk on the Sierpiński graph
    • MR 1378848 97b:60115
    • O. D. Jones, Transition probabilities for the simple random walk on the Sierpiński graph, Stochastic Process. Appl. 61 (1996), 45-69. MR 1378848 (97b:60115)
    • (1996) Stochastic Process. Appl , vol.61 , pp. 45-69
    • Jones, O.D.1
  • 31
    • 0032489697 scopus 로고    scopus 로고
    • The spectral dimension of the branched polymer phase of two-dimensional quantum gravity
    • T. Jonsson and J. F. Wheater, The spectral dimension of the branched polymer phase of two-dimensional quantum gravity, Nuclear Physics B 515 (1998), 549-574.
    • (1998) Nuclear Physics B , vol.515 , pp. 549-574
    • Jonsson, T.1    Wheater, J.F.2
  • 32
    • 0001710365 scopus 로고
    • The incipient infinite cluster in two-dimensional percolation
    • MR 859839 88c:60196
    • H. Kesten, The incipient infinite cluster in two-dimensional percolation, Probab. Theory Related Fields 73 (1986), 369-394. MR 859839 (88c:60196)
    • (1986) Probab. Theory Related Fields , vol.73 , pp. 369-394
    • Kesten, H.1
  • 33
    • 0000367213 scopus 로고
    • Subdiffusive behavior of random walk on a random cluster
    • MR 871905 88b:60232
    • _, Subdiffusive behavior of random walk on a random cluster, Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), 425-487. MR 871905 (88b:60232)
    • (1986) Ann. Inst. H. Poincaré Probab. Statist , vol.22 , pp. 425-487
    • Kesten, H.1
  • 35
    • 0002343091 scopus 로고
    • Harmonic calculus on limits of networks and its application to dendrites
    • MR 1317710 96e:60130
    • J. Kigami, Harmonic calculus on limits of networks and its application to dendrites, J. Funct. Anal. 128 (1995), 48-86. MR 1317710 (96e:60130)
    • (1995) J. Funct. Anal , vol.128 , pp. 48-86
    • Kigami, J.1
  • 36
    • 0038404101 scopus 로고    scopus 로고
    • Analysis on fractals
    • Cambridge University Press, Cambridge, MR 1840042 2002c:28015
    • _, Analysis on fractals, Cambridge Tracts in Mathematics, vol. 143, Cambridge University Press, Cambridge, 2001. MR 1840042 (2002c:28015)
    • (2001) Cambridge Tracts in Mathematics , vol.143
    • Kigami, J.1
  • 37
    • 21844489044 scopus 로고
    • Brownian motion on the continuum tree
    • MR 1324094 96b:60214
    • W. B. Krebs, Brownian motion on the continuum tree, Probab. Theory Related Fields 101 (1995), 421-433. MR 1324094 (96b:60214)
    • (1995) Probab. Theory Related Fields , vol.101 , pp. 421-433
    • Krebs, W.B.1
  • 39
    • 2942590208 scopus 로고    scopus 로고
    • V. Sidoravicius and A.-S. Sznitman, Quenched invariance principles for walks on clusters of percolation or among random conductances, Probab. Theory Related Fields 129 (2004), 219-244. MR 2063376 (2005d:60155)
    • V. Sidoravicius and A.-S. Sznitman, Quenched invariance principles for walks on clusters of percolation or among random conductances, Probab. Theory Related Fields 129 (2004), 219-244. MR 2063376 (2005d:60155)


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