Universal Persistence for Local Time of One-dimensional Random Walk

Jing Miao, Amir Dembo

We prove the power law decay $p(t,x)\sim t^{-\varphi (x,b)/2}$ in which $p(t,x)$ is the probability that the fraction of time up to $t$ in which a random walk $S$ of i.i.d. zero-mean inc…