3 problems

Let $\mathbf{T}$ be a critical binary branching Galton–Watson tree, and let $S_{\mathbf{T}}$ be a $\mathbb{Z}^4$-valued branching random walk with centred, nearest-neighbour increm…

Let $l_x^N$ be the total local time at $x$ for a simple random walk on $\mathbb{Z}^2$ started at the origin and stopped when it leaves $[-N,N]^2\cap\mathbb{Z}^2$, and let $\nu'$ de…

Let $A_a$ be the set of $a$-thick points of planar Brownian motion. The known lower bound is $\dim(A_a)\geq 2-a$ almost surely for $a\in(0,1/2)$. Bass, Burdzy and Khoshnevisan's th…