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arXiv · 2502.18964

Variational representation and estimates for the free energy of a quenched charged polymer model

Julien Poisat
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Abstract

Random walks with a disordered self-interaction potential may be used to model charged polymers. In this paper we consider a one-dimensional and directed version of the charged polymer model that was introduced by Derrida, Griffiths and Higgs. We prove new results for the associated quenched free energy, including a variational formula based on a quenched large deviation principle established by Birkner, Greven and den Hollander. We also take the occasion to (i) provide detailed proofs for state-of-the-art results pointing towards the existence of a freezing transition and (ii) proceed with minor corrections for two results previously obtained by the present author with Caravenna, den Hollander and P{é}tr{é}lis for the undirected model.

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Julien Poisat. 2025-02-26. Variational representation and estimates for the free energy of a quenched charged polymer model. https://arxiv.org/abs/2502.18964

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