Some sufficient conditions for infinite collisions of simple random walks on a wedge comb

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In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile {f(n), n∈ }. One interesting result is that if f(n) has a growth order as n n, then two independent simple random walks on the wedge comb will collide infinitely many times. Another is that if {f(n); n∈ } are given by i.i.d. non-negative random variables with finite mean, then for almost all wedge comb with such profile, three independent simple random walks on it will collide infinitely many times.