Quantitative stochastic homogenization for random conductance models with stable-like jumps

Xin Chen; Zhen Qing Chen; Takashi Kumagai; Jian Wang

doi:10.1007/s00440-024-01354-5

Quantitative stochastic homogenization for random conductance models with stable-like jumps

Xin Chen
, Zhen Qing Chen
, Takashi Kumagai
, Jian Wang^*

^*Corresponding author for this work

Shanghai Jiao Tong University
University of Washington
Waseda University
Fujian Normal University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider random conductance models with long range jumps on Zd, where the one-step transition probability from x to y is proportional to wx,y|x-y|-d-α with α∈(0,2). Assume that {wx,y}(x,y)∈E are independent, identically distributed and uniformly bounded non-negative random variables with Ewx,y=1, where E is the set of all unordered pairs on Zd. We obtain a quantitative version of stochastic homogenization for these random walks, with explicit polynomial rates up to logarithmic corrections.

Original language	English
Pages (from-to)	627-669
Number of pages	43
Journal	Probability Theory and Related Fields
Volume	191
Issue number	1
DOIs	https://doi.org/10.1007/s00440-024-01354-5
Publication status	Published - Feb 2025
Externally published	Yes

Keywords

Long range jumps
Random conductance model
Stochastic homogenization
α-Stable-like process

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10.1007/s00440-024-01354-5

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title = "Quantitative stochastic homogenization for random conductance models with stable-like jumps",

abstract = "We consider random conductance models with long range jumps on Zd, where the one-step transition probability from x to y is proportional to wx,y|x-y|-d-α with α∈(0,2). Assume that \{wx,y\}(x,y)∈E are independent, identically distributed and uniformly bounded non-negative random variables with Ewx,y=1, where E is the set of all unordered pairs on Zd. We obtain a quantitative version of stochastic homogenization for these random walks, with explicit polynomial rates up to logarithmic corrections.",

keywords = "Long range jumps, Random conductance model, Stochastic homogenization, α-Stable-like process",

author = "Xin Chen and Chen, \{Zhen Qing\} and Takashi Kumagai and Jian Wang",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.",

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doi = "10.1007/s00440-024-01354-5",

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AU - Chen, Xin

AU - Chen, Zhen Qing

AU - Kumagai, Takashi

AU - Wang, Jian

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

PY - 2025/2

Y1 - 2025/2

N2 - We consider random conductance models with long range jumps on Zd, where the one-step transition probability from x to y is proportional to wx,y|x-y|-d-α with α∈(0,2). Assume that {wx,y}(x,y)∈E are independent, identically distributed and uniformly bounded non-negative random variables with Ewx,y=1, where E is the set of all unordered pairs on Zd. We obtain a quantitative version of stochastic homogenization for these random walks, with explicit polynomial rates up to logarithmic corrections.

AB - We consider random conductance models with long range jumps on Zd, where the one-step transition probability from x to y is proportional to wx,y|x-y|-d-α with α∈(0,2). Assume that {wx,y}(x,y)∈E are independent, identically distributed and uniformly bounded non-negative random variables with Ewx,y=1, where E is the set of all unordered pairs on Zd. We obtain a quantitative version of stochastic homogenization for these random walks, with explicit polynomial rates up to logarithmic corrections.

KW - Long range jumps

KW - Random conductance model

KW - Stochastic homogenization

KW - α-Stable-like process

UR - https://www.scopus.com/pages/publications/85213540671

U2 - 10.1007/s00440-024-01354-5

DO - 10.1007/s00440-024-01354-5

M3 - Article

AN - SCOPUS:85213540671

SN - 0178-8051

VL - 191

SP - 627

EP - 669

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

ER -

Quantitative stochastic homogenization for random conductance models with stable-like jumps

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Keywords

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