Stochastic integrability of heat-kernel bounds for random walks in a balanced random environment

2022/09/28 by Xiaoqin Guo, Guo, Xiaoqin, Hung V. Tran +1 · 2 citations
Decision Sciences · Mathematics · #35J15 35J25 35K10 35K20 60G50 60J65 60K37 74Q20 76M50 #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.14293

openalex publication_date 2022/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider random walks in a balanced i.i.d. random environment in Z^d for d≥2 and the corresponding discrete non-divergence form difference operators. We first obtain an exponential integrability of the heat kernel bounds. We then prove the optimal diffusive decay of the semigroup generated by the heat kernel for d≥3. As a consequence, we deduce a functional central limit theorem for the environment viewed from the particle.

Cited by

• Homogenization of non-divergence form operators in i.i.d. random environments
• Numerical approximation of effective diffusivities in homogenization of nondivergence-form equations with large drift by a Lagrangian method

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