1
|
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
| |
Collapse
|
2
|
Gu C. An efficient algorithm for solving elliptic problems on percolation clusters. ANN APPL PROBAB 2022. [DOI: 10.1214/21-aap1748] [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)
- Chenlin Gu
- DMA, Ecole Normale Supérieure, PSL University
| |
Collapse
|
3
|
Bowditch AM, Croydon DA. Biased random walk on supercritical percolation: anomalous fluctuations in the ballistic regime. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp794] [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)
- Adam M. Bowditch
- School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland
| | - David A. Croydon
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| |
Collapse
|
4
|
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
| |
Collapse
|
5
|
Pacheco-Pozo A, Sokolov IM. Convergence to a Gaussian by Narrowing of Central Peak in Brownian yet Non-Gaussian Diffusion in Disordered Environments. PHYSICAL REVIEW LETTERS 2021; 127:120601. [PMID: 34597078 DOI: 10.1103/physrevlett.127.120601] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Revised: 07/28/2021] [Accepted: 08/10/2021] [Indexed: 06/13/2023]
Abstract
In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g., biological, systems.
Collapse
Affiliation(s)
- Adrian Pacheco-Pozo
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
- IRIS Adlershof, Zum Großen Windkanal 2, D-12489 Berlin, Germany
| |
Collapse
|
6
|
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
| |
Collapse
|
7
|
Dario P, Gu C. Quantitative homogenization of the parabolic and elliptic Green’s functions on percolation clusters. ANN PROBAB 2021. [DOI: 10.1214/20-aop1456] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Paul Dario
- School of Mathematical Sciences, Tel Aviv University
| | | |
Collapse
|
8
|
Affiliation(s)
- Paul Dario
- School of Mathematical Sciences, Tel Aviv University
| |
Collapse
|
9
|
Bella P, Schäffner M. Quenched invariance principle for random walks among random degenerate conductances. ANN PROBAB 2020. [DOI: 10.1214/19-aop1361] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
10
|
|
11
|
Giunti A, Gu Y, Mourrat JC. Heat kernel upper bounds for interacting particle systems. ANN PROBAB 2019. [DOI: 10.1214/18-aop1279] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
12
|
Biskup M. An invariance principle for one-dimensional random walks among dynamical random conductances. ELECTRON J PROBAB 2019. [DOI: 10.1214/19-ejp348] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
13
|
Tóth B. Quenched central limit theorem for random walks in doubly stochastic random environment. ANN PROBAB 2018. [DOI: 10.1214/18-aop1256] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
14
|
Fribergh A, Popov S. Biased random walks on the interlacement set. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2018. [DOI: 10.1214/17-aihp841] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
15
|
Fribergh A, Kious D. Scaling limits for sub-ballistic biased random walks in random conductances. ANN PROBAB 2018. [DOI: 10.1214/16-aop1159] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
16
|
Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights. Probab Theory Relat Fields 2018. [DOI: 10.1007/s00440-017-0759-z] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
|
17
|
Giunti A, Mourrat JC. Quantitative homogenization of degenerate random environments. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2018. [DOI: 10.1214/16-aihp793] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
18
|
Kozma G, Tóth B. Central limit theorem for random walks in doubly stochastic random environment: ${\mathscr{H}_{-1}}$ suffices. ANN PROBAB 2017. [DOI: 10.1214/16-aop1166] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
19
|
|
20
|
Sapozhnikov A. Random walks on infinite percolation clusters in models with long-range correlations. ANN PROBAB 2017. [DOI: 10.1214/16-aop1103] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
21
|
Mourrat JC, Nolen J. Scaling limit of the corrector in stochastic homogenization. ANN APPL PROBAB 2017. [DOI: 10.1214/16-aap1221] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
22
|
Gu Y, Mourrat JC. On generalized Gaussian free fields and stochastic homogenization. ELECTRON J PROBAB 2017. [DOI: 10.1214/17-ejp51] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
23
|
Mourrat JC, Otto F. Correlation structure of the corrector in stochastic homogenization. ANN PROBAB 2016. [DOI: 10.1214/15-aop1045] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
24
|
Berger N, Cohen M, Rosenthal R. Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments. ANN PROBAB 2016. [DOI: 10.1214/15-aop1038] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
25
|
Barlow M, Burdzy K, Timár Á. Comparison of quenched and annealed invariance principles for random conductance model. Probab Theory Relat Fields 2016. [DOI: 10.1007/s00440-015-0618-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
26
|
Banerjee S, Hoffman C. Random mass splitting and a quenched invariance principle. Stoch Process Their Appl 2016. [DOI: 10.1016/j.spa.2015.09.012] [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: 11/29/2022]
|
27
|
Rousselle A. Recurrence or transience of random walks on random graphs generated by point processes in Rd. Stoch Process Their Appl 2015. [DOI: 10.1016/j.spa.2015.06.002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
28
|
Chen JP, Ugurcan BE. Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs. Stoch Process Their Appl 2015. [DOI: 10.1016/j.spa.2015.07.011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
29
|
Procaccia EB, Rosenthal R, Sapozhnikov A. Quenched invariance principle for simple random walk on clusters in correlated percolation models. Probab Theory Relat Fields 2015. [DOI: 10.1007/s00440-015-0668-y] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
30
|
Benjamini I, Duminil-Copin H, Kozma G, Yadin A. Disorder, entropy and harmonic functions. ANN PROBAB 2015. [DOI: 10.1214/14-aop934] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
31
|
Andres S, Deuschel JD, Slowik M. Invariance principle for the random conductance model in a degenerate ergodic environment. ANN PROBAB 2015. [DOI: 10.1214/14-aop921] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
32
|
Chen ZQ, Croydon DA, Kumagai T. Quenched invariance principles for random walks and elliptic diffusions in random media with boundary. ANN PROBAB 2015. [DOI: 10.1214/14-aop914] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
33
|
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]
|
34
|
Lamacz A, Neukamm S, Otto F. Moment bounds for the corrector in stochastic homogenization of a percolation model. ELECTRON J PROBAB 2015. [DOI: 10.1214/ejp.v20-3618] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | | | - Felix Otto
- Max Planck Institute for Mathematics in the Sciences
| |
Collapse
|
35
|
Rousselle A. Quenched invariance principle for random walks on Delaunay triangulations. ELECTRON J PROBAB 2015. [DOI: 10.1214/ejp.v20-4006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Arnaud Rousselle
- Université de Rouen and Université Paris Ouest Nanterre La Défense
| |
Collapse
|
36
|
Andres S. Invariance principle for the random conductance model with dynamic bounded conductances. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2014. [DOI: 10.1214/12-aihp527] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
37
|
Zhang Z, Zhang L. Scaling limits for one-dimensional long-range percolation: Using the corrector method. Stat Probab Lett 2013. [DOI: 10.1016/j.spl.2013.06.036] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
38
|
Caputo P, Faggionato A, Prescott T. Invariance principle for Mott variable range hopping and other walks on point processes. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2013. [DOI: 10.1214/12-aihp490] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
39
|
Gloria A, Mourrat JC. Quantitative version of the Kipnis–Varadhan theorem and Monte Carlo approximation of homogenized coefficients. ANN APPL PROBAB 2013. [DOI: 10.1214/12-aap880] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
40
|
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]
|
41
|
A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment. Probab Theory Relat Fields 2013. [DOI: 10.1007/s00440-012-0478-4] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
42
|
Beffara V, Duminil-Copin H. Planar percolation with a glimpse of Schramm–Loewner evolution. PROBABILITY SURVEYS 2013. [DOI: 10.1214/11-ps186] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
43
|
|
44
|
Gallesco C, Popov S. Random walks with unbounded jumps among random conductances I: Uniform quenched CLT. ELECTRON J PROBAB 2012. [DOI: 10.1214/ejp.v17-1826] [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]
|
45
|
Mourrat JC. A quantitative central limit theorem for the random walk among random conductances. ELECTRON J PROBAB 2012. [DOI: 10.1214/ejp.v17-2414] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
46
|
|
47
|
Crawford N, Sly A. Simple random walk on long range percolation clusters I: heat kernel bounds. Probab Theory Relat Fields 2011. [DOI: 10.1007/s00440-011-0383-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
48
|
|
49
|
|
50
|
Biskup M, Spohn H. Scaling limit for a class of gradient fields with nonconvex potentials. ANN PROBAB 2011. [DOI: 10.1214/10-aop548] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|