Weak convergence of random walks conditioned to stay away

Zsolt Pajor-Gyulai, Domokos Szász

Let $\{X_n{\}}_{n\in \mathbb{N}}$ be a sequence of i.i.d. random variables in ${\mathbb{Z}}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on $[0,1]$ for which $Y_n(k/…