Fixed-point statistics from spectral measures on tensor envelope categories

Abstract

We prove some old and new convergence statements for fixed-points statistics using tensor envelope categories, such as the Deligne--Knop category of representations of the "symmetric group" $S_t$ for an indeterminate~$t$. We also discuss some arithmetic speculations related to Chebotarev's density theorem.

v3; 20 pages; minor changes after referee report