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Weidner M. Markov chain approximations for nonsymmetric processes. Stoch Process Their Appl 2023. [DOI: 10.1016/j.spa.2023.01.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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Hutchcroft T. Transience and anchored isoperimetric dimension of supercritical percolation clusters. ELECTRON J PROBAB 2023. [DOI: 10.1214/23-ejp905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Affiliation(s)
- Tom Hutchcroft
- California Institute of Technology, United States of America
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Can VH, Croydon DA, Kumagai T. Spectral dimension of simple random walk on a long-range percolation cluster. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- V. H. Can
- Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam
| | - D. A. Croydon
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - T. Kumagai
- Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
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Non-uniformly parabolic equations and applications to the random conductance model. Probab Theory Relat Fields 2021. [DOI: 10.1007/s00440-021-01081-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
AbstractWe study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $$\mathbb Z^d$$
Z
d
. In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.
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