Download this PDF file Fullscreen Fullscreen Off
References
- Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996), no. 2, 1036--1048. MR1404543 (98b:60168)
- Barlow, Martin T. Random walks on supercritical percolation clusters. Ann. Probab. 32 (2004), no. 4, 3024--3084. MR2094438 (2006e:60146)
- M.T. Barlow and J.-D. Deuschel (2007).Quenched invariance principle for the random conductance model with unbounded conductances.In preparation.
- Bass, Richard F. On Aronson's upper bounds for heat kernels. Bull. London Math. Soc. 34 (2002), no. 4, 415--419. MR1897420 (2003c:35054)
- Benjamini, Itai; Mossel, Elchanan. On the mixing time of a simple random walk on the super critical percolation cluster. Probab. Theory Related Fields 125 (2003), no. 3, 408--420. MR1967022 (2004c:60139)
- Berger, Noam; Biskup, Marek. Quenched invariance principle for simple random walk on percolation clusters. Probab. Theory Related Fields 137 (2007), no. 1-2, 83--120. MR2278453 (Review)
- N. Berger, M. Biskup, C.E. Hoffman and G. Kozma (2006). Anomalous heat-kernel decay for random walk among bounded random conductances. Ann. Inst. Henri Poincar\'e (to appear).
- M. Biskup and J.-D. Deuschel, in preparation.
- M. Biskup and H. Spohn (2007). Scaling limit for a class of gradient fields with non-convex potentials. Preprint arxiv:0704.3086.
- Coulhon, T.; Grigor'yan, A.; Pittet, C. A geometric approach to on-diagonal heat kernel lower bounds on groups. Ann. Inst. Fourier (Grenoble) 51 (2001), no. 6, 1763--1827. MR1871289 (2002m:20067)
- De Masi, A.; Ferrari, P. A.; Goldstein, S.; Wick, W. D. Invariance principle for reversible Markov processes with application to diffusion in the percolation regime. Particle systems, random media and large deviations (Brunswick, Maine, 1984), 71--85, Contemp. Math., 41, Amer. Math. Soc., Providence, RI, 1985. MR0814703 (87a:60077)
- De Masi, A.; Ferrari, P. A.; Goldstein, S.; Wick, W. D. An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Statist. Phys. 55 (1989), no. 3-4, 787--855. MR1003538 (91e:60107)
- R. Durrett (1996). Probability Theory and Examples (Third edition),Duxbury Press, Belmont, CA.
- Fontes, L. R. G.; Mathieu, P. On symmetric random walks with random conductances on ${\Bbb Z}\sp d$. Probab. Theory Related Fields 134 (2006), no. 4, 565--602. MR2214905 (2006m:60142)
- Giacomin, Giambattista; Olla, Stefano; Spohn, Herbert. Equilibrium fluctuations for $\nabla\phi$ interface model. Ann. Probab. 29 (2001), no. 3, 1138--1172. MR1872740 (2003c:60161)
- Goel, Sharad; Montenegro, Ravi; Tetali, Prasad. Mixing time bounds via the spectral profile. Electron. J. Probab. 11 (2006), no. 1, 1--26 (electronic). MR2199053 (2007e:60075)
- Grimmett, Geoffrey. Percolation.Second edition.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 321. Springer-Verlag, Berlin, 1999. xiv+444 pp. ISBN: 3-540-64902-6 MR1707339 (2001a:60114)
- Grimmett, G. R.; Marstrand, J. M. The supercritical phase of percolation is well behaved. Proc. Roy. Soc. London Ser. A 430 (1990), no. 1879, 439--457. MR1068308 (91m:60186)
- Kesten, Harry; Zhang, Yu. The probability of a large finite cluster in supercritical Bernoulli percolation. Ann. Probab. 18 (1990), no. 2, 537--555. MR1055419 (91i:60278)
- Kipnis, C.; Varadhan, S. R. S. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104 (1986), no. 1, 1--19. MR0834478 (87i:60038)
- Liggett, T. M.; Schonmann, R. H.; Stacey, A. M. Domination by product measures. Ann. Probab. 25 (1997), no. 1, 71--95. MR1428500 (98f:60095)
- Lovász, László; Kannan, Ravi. Faster mixing via average conductance. Annual ACM Symposium on Theory of Computing (Atlanta, GA, 1999), 282--287 (electronic), ACM, New York, 1999. MR1798047 (2001i:68179)
- Morris, B.; Peres, Yuval. Evolving sets, mixing and heat kernel bounds. Probab. Theory Related Fields 133 (2005), no. 2, 245--266. MR2198701 (2007a:60042)
- P. Mathieu (2006). Quenched invariance principles for random walks with random conductances, J.~Statist. Phys. (to appear).
- P. Mathieu and A.L. Piatnitski (2007).Quenched invariance principles for random walks on percolation clusters. Proc. Roy. Soc. A463, 2287--2307.
- Nash, J. Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80 1958 931--954. MR0100158 (20 #6592)
- C. Rau (2006). Sur le nombre de points visit\'es par une marche al\'eatoire sur un amas infini de percolation, Bull. Soc. Math. France (to appear).
- Sidoravicius, Vladas; Sznitman, Alain-Sol. Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields 129 (2004), no. 2, 219--244. MR2063376 (2005d:60155)

This work is licensed under a Creative Commons Attribution 3.0 License.