Diffusive limit of random walks on tessellations via generalized gradient flows

2022/02/12 by Anastasiia Hraivoronska, Hraivoronska, Anastasiia, Oliver Tse +1
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2202.06024

openalex publication_date 2022/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study asymptotic limits of reversible random walks on tessellations via a variational approach, which relies on a specific generalized-gradient-flow formulation of the corresponding forward Kolmogorov equation. We establish sufficient conditions on sequences of tessellations and jump intensities under which a sequence of random walks converges to a diffusion process with a possibly spatially-dependent diffusion tensor.

Related

• Gradient Flow from a Random Walk in Hilbert Space
• Constructive approach to limit theorems for recurrent diffusive random walks on a strip
• Homogenization of a Random Walk on a Graph in ℝ^d: An approach to predict macroscale diffusivity in media with finescale obstructions and interactions
• Limit theorems and lack thereof for a multilayer random walk mimicking human mobility
• A variational approach to nonlinear and interacting diffusions