Exponents for the number of pairs of ${\alpha}$-favorite points of simple random walk in ${\mathbb Z}^2$

Abstract

We investigate a problem suggested by Dembo, Peres, Rosen, and Zeitouni, which states that the growth exponent of favorite points associated with a simple random walk in ${\mathbb Z}^2$ coincides, on average and almost surely, with those of late points and high points associated with the discrete Gaussian free field.