References & Citations
Mathematics > Probability
Title: The half-space log-Gamma polymer in the bound phase
(Submitted on 17 Oct 2023 (v1), last revised 8 May 2024 (this version, v2))
Abstract: We consider the log-Gamma polymer in the half-space with bulk weights distributed as $\operatorname{Gamma}^{-1}(2\theta)$ and diagonal weights as $\operatorname{Gamma}^{-1}(\alpha+\theta)$ for $\theta>0$ and $\alpha>-\theta$. We show that in the bound phase, i.e., when $\alpha\in (-\theta,0)$, 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.
Submission history
From: Sayan Das [view email][v1] Tue, 17 Oct 2023 03:17:44 GMT (78kb,D)
[v2] Wed, 8 May 2024 12:59:58 GMT (76kb,D)
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