On Comb(Z^2, f_gamma) with f_gamma(z) = floor(log^gamma ||z||_inf), two independent random walks collide finitely often a.s. if gamma > 1 and infinitely often if gamma <= 1; analogous thresholds are proved for fractal and percolation bases.
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Collisions of random walks on comb graphs with a planar base
On Comb(Z^2, f_gamma) with f_gamma(z) = floor(log^gamma ||z||_inf), two independent random walks collide finitely often a.s. if gamma > 1 and infinitely often if gamma <= 1; analogous thresholds are proved for fractal and percolation bases.