# Random walks on finite quantum groups

## TL;DR

This paper investigates the convergence behavior of random walks on finite quantum groups, analyzing their asymptotic states, convergence rates, and the cut-off phenomenon, with a focus on Sekine quantum groups.

## Contribution

It provides bounds on convergence to the Haar state, characterizes possible limit states, and explores the cut-off phenomenon in specific quantum groups.

## Key findings

- Bound the distance to the Haar state for random walks
- Identify all possible limit states as central idempotent states
- Observe the cut-off phenomenon in Sekine finite quantum groups

## Abstract

In this paper we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e. the limit state if it exists. We note that the possible limits are any central idempotent state. We also look at cut-off phenomenon in the Sekine finite quantum groups.