5 problems

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…

Let $n$ be a non-negative integer. For independent standard Brownian bridges $b_0,\ldots,b_{2n}$, define … Here $b$ is a standard Brownian bridge whose average is represented by…

Let $n$ be a non-negative integer. For independent standard Brownian bridges $b_0,\ldots,b_{2n}$, define … Here $\max$ denotes the maximum over the bridge parameter. Let…

Let $n$ be a non-negative integer and let $h_0$ be an arbitrary sufficiently regular continuous function satisfying … For independent standard Brownian bridges $b_1,\ldots,b_n$, de…