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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: 0.7] [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.
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Dario P. Quantitative homogenization of differential forms. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2021. [DOI: 10.1214/20-aihp1111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Paul Dario
- School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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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
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Affiliation(s)
- Paul Dario
- School of Mathematical Sciences, Tel Aviv University
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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]
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