On homogeneous pinning models and penalizations

TL;DR

This paper explores the application of the penalization method to simple polymer models like the pinning model, focusing on martingale analysis and Markovian limits to understand measure changes.

Contribution

It introduces the use of penalization techniques in the context of pinning models, providing new insights into measure transformations and martingale behavior.

Findings

Penalization method effectively describes measure changes in polymer models.

Martingale analysis reveals Markovian limits in pinning models.

Provides a framework for future studies on polymer measure transformations.

Abstract

In this note, we show how the penalization method, introduced in order to describe some non-trivial changes of the Wiener measure, can be applied to the study of some simple polymer models such as the pinning model. The bulk of the analysis is then focused on the study of a martingale which has to be computed as a Markovian limit.