The disconnection exponent for simple random walk

LetS(t) denote a simple random walk inZ2 with integer timet. The disconnection exponent\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar \gamma $$ \end{document} is defined by saying the probability that the path ofS starting at 0 and ending at the circle of radiusn disconnects 0 from infinity decays like\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$n^{ - \bar \gamma } $$ \end{document}. We prove that the disconnection exponent is well-defined and equals the disconnection exponent for Brownian motion which is known to exist.