7 problems

The log-Gamma polymer large deviation conjecture. There exists $\theta_0>0$ such that uniformly for $0<\theta<\theta_0$ and $\epsilon<s<-\theta\psi(\theta)$ for any $\epsilon>0$, w…

Let $\mathpzc{HSLG}$ denote the half-space log-gamma polymer, let $P$ be a down-right path, and let $\theta$ and $\alpha$ be its model parameters. For each … let $z_{v,P}(\cdot)$ b…

Let $Z(n,m)$ denote the point-to-point log-Gamma polymer partition function, and call a process $(h(k))_{k\geq0}$ horizontal-stationary when the solution with initial data…

Consider the half-space log-Gamma polymer with bulk weights distributed as $\operatorname{Gamma}^{-1}(2\theta)$ and diagonal weights as $\operatorname{Gamma}^{-1}(\alpha+\theta)$,…

Let $\alpha>0$, $u>-\alpha$, and let $z_{u,v}$ be the explicitly constructed stationary processes indexed by $v\in(-\alpha,\min(u,0)]$ for the half-space log-gamma polymer. For ini…

Fix $\theta,r>0$ and let $\tilde{f}_N^{LG}$ be the random continuous function from Definition 2. Then, as $N\to\infty$, the random functions $\tilde{f}_N^{LG}$ converge weakly in…

Let $W$ be inverse-gamma distributed with parameter $\gamma>0$, and let $\tilde{U}_{t'}(x')$ and $\tilde{V}_{t'}(x')$ denote the limiting horizontal and vertical ratios of partitio…