Expansion, random walks and sieving in $$S{L_2}({\mathbb{F}_p}[t])$$


Type
Article
Change log
Authors
Abstract

We construct new examples of expander Cayley graphs of finite groups, arising as congruence quotients of non-elementary subgroups of SL2(𝔽p[t]) modulo certain square-free ideals. We describe some applications of our results to simple random walks on such subgroups, specifically giving bounds on the rate of escape of such walks from algebraic subvarieties, the set of squares and the set of elements with reducible characteristic polynomial in SL2(𝔽p[t]).

Description
Keywords
4901 Applied Mathematics, 4903 Numerical and Computational Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Israel Journal of Mathematics
Conference Name
Journal ISSN
0021-2172
1565-8511
Volume Title
215
Publisher
Springer Science and Business Media LLC
Rights
All rights reserved