Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension

L. R. G. Fontes, M. Isopi, C. M. Newman

Let $\tau =({\tau }_i:i\in \mathbb{Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X=(X_t:t\ge 0,X_0=0)$, be a continuous-time…