# Localization for a random walk in slowly decreasing random potential

We consider a continuous time random walk $X$ in random environment on $\Z^+$ such that its potential can be approximated by the function $V: \R^+\to \R$ given by $Vx=\sig Wx -\frac{b}{1-\alf}x^{1-\alf}$ where $\sig W$ a Brownian motion with diffusion coefficient $\sig0$ and parameters $b$, $\alf$ are such that $b0$ and \$0

Author: Christophe Gallesco; Serguei Popov; Gunter M. Schütz

Source: https://archive.org/