Variational representation and estimates for the free energy of a quenched charged polymer model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912247741153280 |
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| author | Poisat, Julien |
| author_facet | Poisat, Julien |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational representation and estimates for the free energy of a quenched charged polymer model Poisat, Julien Probability Disordered Systems and Neural Networks Statistical Mechanics 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. |
| title | Variational representation and estimates for the free energy of a quenched charged polymer model |
| topic | Probability Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2502.18964 |