10 problems

Erdős–Taylor conjecture. For $d=2$, the maximal local time satisfies

Fomin's conjecture. The statement of Fomin's identity extends to nondiscrete Markov processes by passing to a limit in discrete approximations; the same procedure establishes the w…

Let $R(n)=\{S(0),S(1),\ldots,S(n)\}$ be the range of simple random walk up to time $n$. Erdős–Révész conjecture on repeatedly r-visited random-walk ranges. For every integer…

Erdős–Révész conjecture on favourite-site location after positive occupation. Then

Let $V(n)$ denote a favourite site of simple random walk at time $n$, and let $\nu>1$ be the constant from the Brownian favourite-site upper-tail conjecture. For any non-decreasing…

Brownian favourite-site upper-tail conjecture. There exists a constant $\nu>1$ such that

Self-avoiding walk universality conjecture. SAW and SRW should have the same large-scale behaviour when $d>4$ but not when $d<4$.

Jego's conjecture. Under the setup of the source,

Let the vacant set be the set of vertices of the discrete $d$-dimensional torus not visited by a random walk run up to time $uN^d$, where $N$ is the sidelength and $u$ is the time…

Finite-dependence conjecture. The conclusions of Theorem … should remain true for a finitely dependent environment after a suitable modification of ConditionN.