The Critical Curve of the Random Pinning and Copolymer Models at Weak Coupling

TL;DR

This paper analyzes the critical behavior of random pinning and copolymer models with polynomial tail renewal processes, demonstrating universality in their weak coupling critical curves and confirming a conjecture for copolymer models.

Contribution

It provides the first asymptotic characterization of the critical curves in the weak coupling regime, extending results to both pinning and copolymer models and confirming a key conjecture.

Findings

Critical curves exhibit universal asymptotic behavior.

Confirmed conjecture for copolymer models.

Extended analysis to pinning models.

Abstract

We study random pinning and copolymer models, when the return distribution of the underlying renewal process has a polynomial tail with finite mean. We compute the asymptotic behavior of the critical curves of the models in the weak coupling regime, showing that it is universal. This proves a conjecture of Bolthausen, den Hollander and Opoku for copolymer models (ref. [8]), which we also extend to pinning models.