Stochastic Quantization for the fractional Edwards Measure

TL;DR

This paper establishes the existence of a diffusion process with the fractional Edwards measure as its invariant measure, using Dirichlet form techniques in infinite-dimensional Gaussian analysis, applicable for fractional Brownian motion with specific Hurst parameters.

Contribution

It introduces a novel diffusion process for fractional Edwards measures, expanding the mathematical understanding of fractional polymers in stochastic analysis.

Findings

Existence of the diffusion process proven.

Process is invariant under time translations.

Applicable for fractional Brownian motion with $dH<1$.

Abstract

We prove the existence of a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion in dimension $d\in\mathbb{N}$ with Hurst parameter $H\in(0,1)$ fulfilling $dH < 1$. The diffusion is constructed via Dirichlet form techniques in infinite dimensional (Gaussian) analysis. Moreover, we show that the process is invariant under time translations.