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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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3
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Biskup M, Chen X, Kumagai T, Wang J. Quenched invariance principle for a class of random conductance models with long-range jumps. Probab Theory Relat Fields 2021. [DOI: 10.1007/s00440-021-01059-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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4
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Chen X, Kumagai T, Wang J. Random conductance models with stable-like jumps: Quenched invariance principle. ANN APPL PROBAB 2021. [DOI: 10.1214/20-aap1616] [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)
- Xin Chen
- School of Mathematical Sciences, Shanghai Jiao Tong University
| | - Takashi Kumagai
- Research Institute for Mathematical Sciences, Kyoto University
| | - Jian Wang
- College of Mathematics and Informatics & Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA) & Center for Applied Mathematics of Fujian Province (FJNU), Fujian Normal University
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5
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Random systems in ultrametric spaces. ADV APPL PROBAB 2019. [DOI: 10.1017/apr.2018.72] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
AbstractWe discuss percolation and random walks in a class of homogeneous ultrametric spaces together with similarities and differences in ultrametric and Euclidean spaces. We briefly outline the role of these models in the study of interacting systems. Several open problems are presented.
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Transience and Recurrence of Random Walks on Percolation Clusters in an Ultrametric Space. J THEOR PROBAB 2016. [DOI: 10.1007/s10959-016-0691-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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7
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Berger N, Rosenthal R. Random walks on discrete point processes. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2015. [DOI: 10.1214/13-aihp593] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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8
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Estimates on the effective resistance in anisotropic long-range percolation on. Stat Probab Lett 2013. [DOI: 10.1016/j.spl.2013.01.010] [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: 11/21/2022]
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9
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Crawford N, Sly A. Simple random walk on long-range percolation clusters II: Scaling limits. ANN PROBAB 2013. [DOI: 10.1214/12-aop774] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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