Sub-diffusive regimes for long range self-interacting path measures

TL;DR

This paper investigates how long-range self-interactions affect Brownian motion, providing bounds on variance based on interaction strength and decay rate, contributing to understanding complex stochastic processes.

Contribution

It introduces variance bounds for Brownian motion with long-range self-interactions, linking spatial interaction strength and decay order, a novel analytical approach.

Findings

Variance bounds depend on interaction strength and decay order

Long-range interactions significantly influence Brownian motion behavior

Provides a framework for analyzing self-interacting stochastic processes

Abstract

We study Brownian motion perturbed by a long range self-interaction. We provide variance bounds in terms of the spatial interaction strength and the order of time decay.