3 problems

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…

Simultaneous upper LIL conjecture. For every $\epsilon>0$,

Let $Z=(Z_n)_{n\geq 0}$ be a discrete-time random walk on ${\mathbb Z}^d$ with symmetric increment distribution $p$, meaning $p(x)=p(-x)$ for all $x\in{\mathbb Z}^d$. Insert arbitr…