Stochastic dominance of first return times for nearest-neighbor random walks on ${\mathbb{Z}}^d$

Shoou-Ren Hsiau, Ting-Yi Tsai, Yi-Ching Yao

For a $d$-dimensional probability vector $\mathbf{h}=(h_1,\dots ,h_d)$, let $(S_n^{\mathbf{h}}{)}_{n\ge 0}$ be a nearest-neighbor random walk on ${\mathbb{Z}}^d$ such that at each ste…