Stationary inverse-Wishart polymers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909910954934272 |
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| author | Barraquand, Guillaume Ouyang, Zikun |
| author_facet | Barraquand, Guillaume Ouyang, Zikun |
| contents | A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma polymer, recovered when $d=1$. Much of the features of the log-gamma polymer seem to have analogues for higher $d$, although the integrability needs to be better understood. In this paper, we introduce stationary inverse-Wishart polymer models on a quadrant or a strip of $\mathbb Z^2$. In each setting, we identify stationary measures, characterized explicitly in terms of random walks with inverse-Wishart increments in special cases, or more complicated two-layer Gibbs measures for generic choices of boundary parameters. We also make conjectures about asymptotics of the free energy, and explain important differences between matrix-valued polymer models and their scalar counterpart, due to non-commutativity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stationary inverse-Wishart polymers Barraquand, Guillaume Ouyang, Zikun Probability Statistical Mechanics Mathematical Physics A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of $d\times d$ inverse-Wishart random matrices, so that the model nicely generalizes the well-studied log-gamma polymer, recovered when $d=1$. Much of the features of the log-gamma polymer seem to have analogues for higher $d$, although the integrability needs to be better understood. In this paper, we introduce stationary inverse-Wishart polymer models on a quadrant or a strip of $\mathbb Z^2$. In each setting, we identify stationary measures, characterized explicitly in terms of random walks with inverse-Wishart increments in special cases, or more complicated two-layer Gibbs measures for generic choices of boundary parameters. We also make conjectures about asymptotics of the free energy, and explain important differences between matrix-valued polymer models and their scalar counterpart, due to non-commutativity. |
| title | Stationary inverse-Wishart polymers |
| topic | Probability Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2511.14375 |