Existence and Exponential mixing of infinite white $\alpha$-stable Systems with unbounded interactions

TL;DR

This paper investigates infinite white lpha-stable systems with unbounded interactions, establishing their existence through Galerkin approximation and demonstrating exponential mixing via an lpha-stable gradient bounds.

Contribution

It introduces a novel approach to prove existence and exponential mixing for infinite lpha-stable systems with unbounded interactions.

Findings

Existence of the systems proven using Galerkin approximation

Exponential mixing established through lpha-stable gradient bounds

Provides a framework for analyzing similar infinite stochastic systems

Abstract

We study an infinite white $\alpha$-stable systems with unbounded interactions, proving the existence by Galerkin approximation and exponential mixing property by an $\alpha$-stable version of gradient bounds.