Convergence to stationary measures for the half-space log-gamma polymer
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918058241556480 |
|---|---|
| author | Das, Sayan Serio, Christian |
| author_facet | Das, Sayan Serio, Christian |
| contents | We consider the point-to-point half-space log-gamma polymer model in the unbound phase. We prove that the free energy increment process on the anti-diagonal path converges to the top marginal of a two-layer Markov chain with an explicit description, which can be interpreted as two random walks conditioned softly never to intersect. This limiting law is a stationary measure for the polymer on the anti-diagonal path.
The starting point of our analysis is an embedding of the free energy into the half-space log-gamma line ensemble recently constructed by Barraquand, Corwin, and Das. Given the Gibbsian line ensemble structure, the main contribution of our work lies in developing a route to access and prove convergence to stationary measures via line ensemble techniques. Our argument relies on a description of the limiting behavior of two softly non-intersecting random walk bridges around their starting point, a result established in this paper that may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence to stationary measures for the half-space log-gamma polymer Das, Sayan Serio, Christian Probability Mathematical Physics 82D60, 60K35, 82B41 We consider the point-to-point half-space log-gamma polymer model in the unbound phase. We prove that the free energy increment process on the anti-diagonal path converges to the top marginal of a two-layer Markov chain with an explicit description, which can be interpreted as two random walks conditioned softly never to intersect. This limiting law is a stationary measure for the polymer on the anti-diagonal path. The starting point of our analysis is an embedding of the free energy into the half-space log-gamma line ensemble recently constructed by Barraquand, Corwin, and Das. Given the Gibbsian line ensemble structure, the main contribution of our work lies in developing a route to access and prove convergence to stationary measures via line ensemble techniques. Our argument relies on a description of the limiting behavior of two softly non-intersecting random walk bridges around their starting point, a result established in this paper that may be of independent interest. |
| title | Convergence to stationary measures for the half-space log-gamma polymer |
| topic | Probability Mathematical Physics 82D60, 60K35, 82B41 |
| url | https://arxiv.org/abs/2402.16834 |