Ayyer, A and Steinberg, B (2020) Random walks on rings and modules. In: Algebraic Combinatorics, 3 (2). pp. 309-329.
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Abstract
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 ∈ R, b ∈ 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). © 2020 Centre Mersenne NORMAL.
| Item Type: | Journal Article |
|---|---|
| Publication: | Algebraic Combinatorics |
| Publisher: | Centre Mersenne |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Modules; Monoids; Random walks; Representation theory; Rings |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 23 Jan 2023 09:59 |
| Last Modified: | 23 Jan 2023 09:59 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79258 |
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