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Positive definite functions and cut-off for discrete groups
Canadian Mathematical Bulletin ( IF 0.6 ) Pub Date : 2020-06-22 , DOI: 10.4153/s0008439520000466
Amaury Freslon

We consider the sequence of powers of a positive definite function on a discrete group. Taking inspiration from random walks on compact quantum groups, we give several examples of situations where a cut-off phenomenon occurs for this sequence with respect to the operator norm of the regular representation, including free groups and infinite Coxeter groups. We also give examples of absence of cut-off using free groups again.

中文翻译:

离散群的正定函数和截止

我们考虑离散群上正定函数的幂序列。从紧致量子群上的随机游走中汲取灵感,我们给出了几个例子,说明这个序列相对于正则表示的算子范数发生截止现象的情况,包括自由群和无限 Coxeter 群。我们还再次使用自由组给出了没有截止的例子。
更新日期:2020-06-22
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