16 problems

Let $\tilde{\beta}$, $\tilde{t}$, $\alpha$, and $A$ be the parameters from the cited high-density asymptotic theorem, and let $\widetilde{Q}_{\tilde{\beta}<\tilde{t}}^{High}$ be th…

Consider planar last-passage percolation with geometric weights. Let $T_n(\omega)$ and $T_n(\tilde\omega^t)$ denote the last-passage times in the original and site-resampled enviro…

Conditional geodesic fluctuation conjecture. Conditional on $\mathcal L(aN,bN)=\ell N$,

Conditional fluctuation conjecture. The following hold. For $(x,y)\in\Omega_1$, the centered passage time has Tracy–Widom $\operatorname{TW}_2$ fluctuations on the $N^{1/3}$ scale…

Conditional law of large numbers conjecture. The convergence in the conditional law of large numbers holds with

Let $\frac12\log q<0$, with $[?]$?

Fix a dynamical last passage percolation model, and let $\mathscr{T}$ be the set of times at which non-trivial bigeodesics exist. Hausdorff-dimension-zero conjecture. The set…

ASEP backward-geodesic endpoint conjecture. For any $N\in\mathbb{Z}$,

Let $T_0$ and $T_t$ be the passage times at perturbation times $0$ and $t$, and write $\operatorname{Var}(T)$ for the variance of the passage time and…

Let $T_0$ and $T_t$ be the passage times at perturbation times $0$ and $t$, and let $\pi_0$ and $\pi_t$ be the corresponding geodesics. Write $\operatorname{Var}(T)$ for the varian…

Let $T_0,\dots,T_{n-1}$ be the absorption times in the type $B$ oriented swap process, and let $L((0,0),(u,v))$ denote the corresponding half-space LPP passage time. Type B distrib…

Let $\{B_i(\cdot)\}_{i\in\mathbb{Z}}$ be a sequence of two-sided standard Brownian motions on $\mathbb{R}$, and let $\Pi_n$ be the almost surely unique geodesic from $(0,0)$ to…

Let $\bm{U}_n$ denote the vector of oriented swap process finishing times and let $\bm{V}_n$ denote the point-to-line last passage percolation vector. The oriented swap process–LPP…

Let $\mathbf{U}_N=(U_N(1),\dots,U_N(N-1))$ be the vector of swap-passage times in the oriented swap process, and let $\mathbf{V}_N=(V_N(1),\dots,V_N(N-1))$ be the vector of last-pa…

Let $(X_{i,j})_{i,j\ge 1}$ be an array of independent, identically distributed exponential random variables of rate $1$. For each $n\ge 2$, let $\bm{V}_n$ denote the vector of last…

Let $\mathcal{A}$ be the Airy line ensemble, and define $\mathcal{H}:\mathbb{R}^2\to\mathbb{R}$ deterministically from $\mathcal{A}$ by the formulas in the source on…