1
|
Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2021.08.006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
2
|
Lower Gaussian heat kernel bounds for the random conductance model in a degenerate ergodic environment. Stoch Process Their Appl 2021. [DOI: 10.1016/j.spa.2021.05.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
3
|
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: 0.7] [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.
Collapse
|
4
|
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]
|
5
|
Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights. Probab Theory Relat Fields 2021. [DOI: 10.1007/s00440-021-01028-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
AbstractWe establish a quenched local central limit theorem for the dynamic random conductance model on $${\mathbb {Z}}^d$$
Z
d
only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show Hölder continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with time-dependent degenerate weights. The proof is based on De Giorgi’s iteration technique. In addition, we also derive a quenched local central limit theorem for the static random conductance model on a class of random graphs with degenerate ergodic weights.
Collapse
|
6
|
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
|
7
|
Deuschel JD, Fukushima R. Quenched tail estimate for the random walk in random scenery and in random layered conductance II. ELECTRON J PROBAB 2020. [DOI: 10.1214/20-ejp478] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
8
|
Andres S, Deuschel JD, Slowik M. Green kernel asymptotics for two-dimensional random walks under random conductances. ELECTRONIC COMMUNICATIONS IN PROBABILITY 2020. [DOI: 10.1214/20-ecp337] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
9
|
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]
|