|
51
|
|
|
52
|
Quenched invariance principle for random walks in balanced random environment. Probab Theory Relat Fields 2010. [DOI: 10.1007/s00440-010-0320-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
|
|
53
|
Fribergh A. The speed of a biased random walk on a percolation cluster at high density. ANN PROBAB 2010. [DOI: 10.1214/09-aop521] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
54
|
Comets F, Popov S, Schütz GM, Vachkovskaia M. Quenched invariance principle for the Knudsen stochastic billiard in a random tube. ANN PROBAB 2010. [DOI: 10.1214/09-aop504] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
55
|
Barlow MT, Deuschel JD. Invariance principle for the random conductance model with unbounded conductances. ANN PROBAB 2010. [DOI: 10.1214/09-aop481] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
56
|
|
|
57
|
Boukhadra O. Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances Model. ELECTRON J PROBAB 2010. [DOI: 10.1214/ejp.v15-839] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
58
|
Faggionato A. Hydrodynamic Limit of Zero Range Processes Among Random Conductances on the Supercritical Percolation Cluster. ELECTRON J PROBAB 2010. [DOI: 10.1214/ejp.v15-748] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
59
|
Barlow MT, Černý J. Convergence to fractional kinetics for random walks associated with unbounded conductances. Probab Theory Relat Fields 2009. [DOI: 10.1007/s00440-009-0257-z] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
|
60
|
|
|
61
|
Caputo P, Faggionato A. Diffusivity in one-dimensional generalized Mott variable-range hopping models. ANN APPL PROBAB 2009. [DOI: 10.1214/08-aap583] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
62
|
Hambly B, Barlow M. Parabolic Harnack inequality and local limit theorem for percolation clusters. ELECTRON J PROBAB 2009. [DOI: 10.1214/ejp.v14-587] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
63
|
Goncalves P, Jara M. Density fluctuations for a zero-range process on the percolation cluster. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2009. [DOI: 10.1214/ecp.v14-1491] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
64
|
Kumagai T, Misumi J. Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media. J THEOR PROBAB 2008. [DOI: 10.1007/s10959-008-0183-5] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
|
65
|
Deuschel JD, Kösters H. The quenched invariance principle for random walks in random environments admitting a bounded cycle representation. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2008. [DOI: 10.1214/07-aihp122] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
66
|
Berger N, Biskup M, Hoffman CE, Kozma G. Anomalous heat-kernel decay for random walk among bounded random conductances. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2008. [DOI: 10.1214/07-aihp126] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
67
|
Pete G. A note on percolation on $Z^d$: isoperimetric profile via exponential cluster repulsion. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2008. [DOI: 10.1214/ecp.v13-1390] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
68
|
Faggionato A. Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit. ELECTRON J PROBAB 2008. [DOI: 10.1214/ejp.v13-591] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
69
|
Caputo P, Faggionato A. Isoperimetric inequalities and mixing time for a random walk on a random point process. ANN APPL PROBAB 2007. [DOI: 10.1214/07-aap442] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
|
70
|
Mathieu P, Piatnitski A. Quenched invariance principles for random walks on percolation clusters. Proc Math Phys Eng Sci 2007. [DOI: 10.1098/rspa.2007.1876] [Citation(s) in RCA: 88] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We consider a supercritical Bernoulli percolation model in
,
d
≥2, and study the simple symmetric random walk on the infinite percolation cluster. The aim of this paper is to prove the almost sure (quenched) invariance principle for this random walk.
Collapse
Affiliation(s)
- P Mathieu
- Université de Provence, CMI, 39 rue Joliot-Curie13013 Marseille, France
| | - A Piatnitski
- Lebedev Physical Institute of Russian Academy of Sciences and Narvik Institute of Technology, PO Box 3858505 Narvik, Norway
| |
Collapse
|
|
71
|
|
|
72
|
Biskup M, Prescott T. Functional CLT for Random Walk Among Bounded Random Conductances. ELECTRON J PROBAB 2007. [DOI: 10.1214/ejp.v12-456] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|