2 problems

Let $M_\gamma$ be the periodic TASEP Markov matrix, and let $\lambda_2(\gamma)$ denote its second-largest eigenvalue. For sufficiently small $|\gamma|$, the largest eigenvalue is o…

Let $F(x;\tau,\gamma)$ denote the one-point distribution for periodic TASEP, let $F_{\mathrm{GUE}}$ denote the GUE Tracy–Widom distribution, and let $x\in\mathbb R$. The parameters…