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

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