arXiv Analytics

Sign in

arXiv:1708.04223 [math.CO]AbstractReferencesReviewsResources

Random walks on rings and modules

Arvind Ayyer, Benjamin Steinberg

Published 2017-08-14Version 1

We consider two natural models of random walks on a module $V$ over a finite commutative ring $R$ driven simultaneously by addition of random elements in $V$, and multiplication by random elements in $R$. In the coin-toss walk, either one of the two operations is performed depending on the flip of a coin. In the affine walk, random elements $a \in R,b \in V$ are sampled independently, and the current state $x$ is taken to $ax+b$. For both models, we obtain the complete spectrum of the transition matrix from the representation theory of the monoid of all affine maps on $V$ under a suitable hypothesis on the measure on $V$ (the measure on $R$ can be arbitrary).

Related articles: Most relevant | Search more
arXiv:1401.4250 [math.CO] (Published 2014-01-17, updated 2014-09-03)
Markov chains, $\mathscr R$-trivial monoids and representation theory
arXiv:1508.05446 [math.CO] (Published 2015-08-22)
Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry
arXiv:1805.00113 [math.CO] (Published 2018-04-30)
Identities from representation theory