7 problems

Let $D$ be a domain, let $0$ be a point whose accessibility from $D$ is considered, and consider the corresponding conditional symmetric $\alpha$-stable Lévy process at its lifetim…

In dimensions $d\leq 3$, let the infinite snake be the branching random walk conditioned to be infinite, subsequently conditioned never to reach the origin, whenever this condition…

General-potential conditioning conjecture. As $T\to\infty$, the probability measures

Entropic-repulsion conjecture. If $g$ is strictly below the fluctuations of Brownian motion, then the limiting process conditioned on the corresponding restriction involving…

Let $G=(V,E)$ be a locally finite, connected, transitive, transient graph with spectral radius $\rho$, fix $o\in V$, and let $(X_n)_{n\geq 0}$ be simple random walk started at $o$.…

Let $v$ be a parameter in the general approximation framework, with stopping times $\tau_a^v\to\infty$ and events $\mathcal{E}_a^v$ such that the conditioned measures converge to…

Persistence conjecture. The extra branching remains negligible for a few generations, corresponding roughly to the second term in the definition of $\gamma(\varepsilon)$, and after…