3 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 $\alpha>0$, $u>-\alpha$, 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…