Self-avoiding fractional Brownian motion - The Edwards model

TL;DR

This paper extends the Edwards polymer model to fractional Brownian motions in multiple dimensions, broadening the mathematical understanding of self-avoiding stochastic processes with long-range dependence.

Contribution

It generalizes Varadhan's construction of the Edwards model to fractional Brownian motions across various dimensions and Hurst parameters.

Findings

Successful extension of the Edwards model to fractional Brownian motion

Applicable to dimensions d ≥ 2 and Hurst parameters H ≤ 1/d

Provides a new framework for analyzing self-avoiding stochastic processes

Abstract

In this work we extend Varadhan's construction of the Edwards polymer model to the case of fractional Brownian motions in $\R^d$, for any dimension $d\geq 2$, with arbitrary Hurst parameters $H\leq 1/d$.