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We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range correlations introduced in arXiv:1212.2885, solving one of the open problems from there.
J. Nash (1958) Continuity of solutions of parabolic and elliptic equations. Amer. J. Math
1958
Earlier work this paper cites.
G. F. Lawler (1982/83) Weak convergence of a random walk in a random environment. Comm. Math. Phys
1982
Earlier work this paper cites.
A. De Masi, P. A. Ferrari, S. Goldstein, and W. D. Wick (1985) Invariance principle for reversible Markov processes with application to diffusion in the percolation regime. In Particle systems, random media and large deviations (Brunswick, Maine, 1984), Contemp. Math
1985
Earlier work this paper cites.
J. L. Lebowitz and H. Saleur (1986) Percolation in strongly correlated systems. Phys. A
1986
Earlier work this paper cites.
J. Bricmont, J. L. Lebowitz and C. Maes (1987) Percolation in strongly correlated systems: the massless Gaussian field. J. Stat. Phys
1987
Earlier work this paper cites.
A. De Masi, P. A. Ferrari, S. Goldstein, and W. D. Wick (1989) An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Statist. Phys
1989
Earlier work this paper cites.
J. D. Deuschel and A. Pisztora (1996) Surface order large deviations for high-density percolation. Probab. Theory Related Fields
1996
Earlier work this paper cites.
T. M. Liggett, R. H. Schonmann, and A. M. Stacey (1997) Domination by product measures. Ann. Probab
1997
Earlier work this paper cites.
R. F. Bass (2002) On Aronson’s upper bounds for heat kernels. Bull. London Math. Soc
2002
Earlier work this paper cites.
I. Benjamini and E. Mossel (2003) On the mixing time of a simple random walk on the super critical percolation cluster. Probab. Theor. Rel. Fields
2003
Earlier work this paper cites.
M. T. Barlow (2004) Random walks on supercritical percolation clusters. Ann. Probab
2004
Earlier work this paper cites.
P. Mathieu and E. Remy (2004) Isoperimetry and heat kernel decay on percolations clusters. Ann. Probab
2004
Earlier work this paper cites.
V. Sidoravicius and A.-S. Sznitman (2004) Quenched invariance principles for walks on clusters of percolation or among random conductances. Prob. Th. Rel. Fields
2004
Cited alongside, same era.
N. Berger and M. Biskup (2007) Quenched invariance principle for simple random walk on percolation cluster. Probab. Theory Rel. Fields
2007
Cited alongside, same era.
M. Biskup and T. Prescott (2007) Functional CLT for random walk among bounded random conductances. Electron. J. Probab
2007
Cited alongside, same era.
P. Mathieu and A. L. Piatnitski (2007) Quenched invariance principles for random walks on percolation clusters. Proceedings of the Royal Society A
2007
Cited alongside, same era.
N. Berger, M. Biskup, C. Hoffman and G. Kozma (2008) Anomalous heat-kernel decay for random walk on among bounded random conductances. Ann. Inst. H. Poincaré Probab. Statist
A. Drewitz, B. Ráth and A. Sapozhnikov (2012) On chemical distances and shape theorems in percolation models with long-range correlations. J. Math. Phys
2012
Later among the works it cites.
X. Guo and O. Zeitouni (2012) Quenched invariance principle for random walks in balanced random environment. Probab. Theory Related Fields
2012
Later among the works it cites.
2012
Later among the works it cites.
P. F. Rodriguez and A.-S. Sznitman (2012) Phase transition and level-set percolation for the Gaussian free field. Comm. Math. Phys
2012
Later among the works it cites.
A.-S. Sznitman (2012) Decoupling inequalities and interlacement percolation on G × ℤ G\times{\mathbb{Z}} . Invent. Math
2012
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2008
Cited alongside, same era.
P. Mathieu (2008) Quenched invariance principles for random walks with random conductances. J. Stat. Phys
2008
Cited alongside, same era.
G. Pete (2008) A note on percolation on ℤ d {\mathbb{Z}}^{d} : Isoperimetric profile via exponential cluster repulsion. Electron. Commun. Probab
2008
Cited alongside, same era.
V. Sidoravicius and A.-S. Sznitman (2009) Percolation for the Vacant Set of Random Interlacements. Comm. Pure Appl. Math
2009
Cited alongside, same era.
M. T. Barlow and J.-D. Deuschel (2010) Invariance principle for the random conductance model with unbounded conductances. Ann. Probab
2010
Cited alongside, same era.
M. Biskup (2011) Recent progress on the Random Conductance Model. Prob. Surveys
2011
Cited alongside, same era.
B. Ráth and A. Sapozhnikov (2011) The effect of small quenched noise on connectivity properties of random interlacements. Electron. J. of Prob
2011
Cited alongside, same era.
A. Drewitz, B. Ráth and A. Sapozhnikov (2012) Local percolative properties of the vacant set of random interlacements with small intensity. Ann. Inst. H. Poincaré Probab. Statist
2012
Cited alongside, same era.
Later among the works it cites.
S. Andres, M. T. Barlow, J.-D. Deuschel, and B. M. Hambly (2013) Invariance principle for the random conductance model. Probab. Theory Related Fields
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