3 problems

Exceptional-time conjecture. Almost surely, exceptional times at which $\mathcal{C}_t$ contains an unbounded component exist, and the Hausdorff dimension of the random set of such…

Let $F$ be a three-dimensional Bargmann–Fock field on $\mathbb{R}^3$. For each $t\in\mathbb{R}$, let $f^{\mathrm{hor}}(t)$ be the two-dimensional Bargmann–Fock field obtained by re…

Let $\mathcal{D}_p$ denote the excursion domain at level $p$ associated with a centered, normalized, non-degenerate, sufficiently smooth, stationary, isotropic, and positively corr…