Abstract
where IG[ is the order of G and P" is the nth convolut ion power of P. They show that this is a natural tool for studying strong uniform times for r a n d o m walks on G, and they show in Theorem 7 of [1] (stated as Theorem 5 in [-7, Chap. 4C]) that if I[P'-ml[~O as n ~ , then s(n)~O as n ~ at a rate that depends on how fast l iP ' -m[[ converges to 0 but does not depend on the size of the group G. In particular, if J[P"-m[[ is small then s(2n) is small.
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