The half-space log-Gamma polymer in the bound phase
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909194374873088 |
|---|---|
| author | Das, Sayan Zhu, Weitao |
| author_facet | Das, Sayan Zhu, Weitao |
| contents | We consider the log-Gamma polymer in the half-space with bulk weights distributed as $\operatorname{Gamma}^{-1}(2θ)$ and diagonal weights as $\operatorname{Gamma}^{-1}(α+θ)$ for $θ>0$ and $α>-θ$. We show that in the bound phase, i.e., when $α\in (-θ,0)$, the endpoint of the polymer lies within an $O(1)$ stochastic window of the diagonal. This result gives the first rigorous proof of the pinned phenomena for the half-space polymers in the bound phase conjectured by Kardar(1985). We also show that the limiting quenched endpoint distribution of the polymer around the diagonal is given by a random probability mass function proportional to the exponential of a random walk with log-Gamma type increments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10960 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The half-space log-Gamma polymer in the bound phase Das, Sayan Zhu, Weitao Probability We consider the log-Gamma polymer in the half-space with bulk weights distributed as $\operatorname{Gamma}^{-1}(2θ)$ and diagonal weights as $\operatorname{Gamma}^{-1}(α+θ)$ for $θ>0$ and $α>-θ$. We show that in the bound phase, i.e., when $α\in (-θ,0)$, the endpoint of the polymer lies within an $O(1)$ stochastic window of the diagonal. This result gives the first rigorous proof of the pinned phenomena for the half-space polymers in the bound phase conjectured by Kardar(1985). We also show that the limiting quenched endpoint distribution of the polymer around the diagonal is given by a random probability mass function proportional to the exponential of a random walk with log-Gamma type increments. |
| title | The half-space log-Gamma polymer in the bound phase |
| topic | Probability |
| url | https://arxiv.org/abs/2310.10960 |