9 problems

Let $X$ be a random walk in Dirichlet environment, and let $\mathbf{(T')}$ denote Sznitman's condition in a unit direction $\hat u$: directional transience means … and the renewal-…

Let $X$ be a random walk in Dirichlet environment on ${\mathbb Z}^2$ with drift vector $d_\alpha=\sum_{i=1}^4\alpha_i e_i$. A walk is directionally transient in a unit direction…

Let $G$ be a transitive transient graph. For $\varepsilon>0$, let an $\varepsilon$-$\operatorname{WUSF}$ be obtained by independently retaining each edge of a wired uniform spannin…

Fix $d\ge 3$ and consider the $d$-dimensional lattice ${\mathbb Z}^d$ with nonnegative symmetric edge weights $W_{ij}$ satisfying … and … The associated VRJP is known in the source…

Decay-exponent conjecture. The positive-probability transience result should hold for every

Transience and growth conjecture. The walk should satisfy

Let $G$ be a transitive transient graph, and consider Bernoulli percolation on $G$ with a parameter above the critical threshold, so that an infinite cluster exists. Benjamini–Lyon…

Let $X$ be the increment random variable of the random walk in $\mathbb{R}^d$, and let $G_n$ denote its centre of mass after $n$ steps. Assume that the support of $X$ is not contai…

Let $P$ be a distribution on environments satisfying Assumption asmiid, and suppose that … Here, $\mathfrak{R}$ denotes the first return time to the origin, and $X_1$ is the first…