4 problems

A Brownian Gibbs $\mathbb{N}$-indexed line ensemble is a random collection of curves $\mathcal{L}=(\mathcal{L}_i)_{i\in\mathbb{N}}$ satisfying the Brownian Gibbs property. Define t…

At positive temperature, last passage percolation is replaced by directed polymers: sums over non-intersecting random walks are weighted by products of weights along their trajecto…

KPZ line ensemble convergence conjecture. As $t\to\infty$, the line ensemble $\{\mathcal{L}^{t}_n(x)\}$ converges, in the sense of line ensembles, to the Airy line ensemble…

Let $\mathcal{A}$ be an $\mathbb{N}$-indexed line ensemble. Say that $\mathcal{A}$ is $x$-invariant if $\mathcal{A}(s+cdot)$ has the same distribution as $\mathcal{A}$ for every…