The martingale approach to disorder irrelevance for pinning models

TL;DR

This paper provides a straightforward proof demonstrating that disorder does not affect the critical behavior of certain pinning models with specific return exponents, and introduces a new upper bound for contact fraction at criticality.

Contribution

It offers a simple, self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent in (0,1/2) and establishes a new upper bound for contact fraction at criticality.

Findings

Disorder irrelevance proven for models with return exponent in (0,1/2)

New upper bound for contact fraction at criticality

Simplified proof technique for disorder effects in pinning models

Abstract

This paper presents a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent alpha in the Interval (0,1/2). We also give a new upper bound for the contact fraction of the disordered model at criticality.