Tightness conditions for polymer measures

TL;DR

This paper establishes conditions ensuring tightness of probability measures for polymer models, facilitating analysis of their convergence properties, with applications to various random walk models for polymers and interfaces.

Contribution

It provides new sufficient tightness conditions for polymer measures with decoupling properties, applicable to diverse random walk models.

Findings

Established tightness conditions for polymer measures.

Applied results to homogeneous, periodic, and disordered random walk models.

Enhanced understanding of polymer measure convergence.

Abstract

We give sufficient conditions for tightness in the space C([0,1]) for sequences of probability measures which enjoy a suitable decoupling between zero level set and excursions. Applications of our results are given in the context of (homogeneous, periodic and disordered) random walk models for polymers and interfaces.