The Edwards Model for fBm Loops and Starbursts

TL;DR

This paper extends the Edwards polymer model to fractional Brownian loops and starbursts, demonstrating that the Edwards density remains integrable under renormalization for certain Hurst parameters.

Contribution

It introduces a generalized Edwards model for fractional Brownian structures, expanding the mathematical framework for polymer modeling.

Findings

Edwards density is integrable for H<= 1/d after renormalization

Extension of Varadhan's construction to fractional Brownian loops and starbursts

Provides conditions for the integrability of the Edwards density in fractional settings

Abstract

We extend Varadhan's construction of the Edwards polymer model to fractional Brownian loops and fractional Brownian starbursts. We show that, as in the fBm case, the Edwards density under a renormalizaion is an integrable function for the case H<= 1/d.