A quenched limit theorem for the local time of random walks on \Z^2

Jürgen Gärtner, Rongfeng Sun

Let $X$ and $Y$ be two independent random walks on ${\mathbb{Z}}^2$ with zero mean and finite variances, and let $L_t(X,Y)$ be the local time of $X-Y$ at the origin at time $t$. We show that…