Random walks on finite groups converging after finite number of steps

• Main Authors: Vyshnevetskiy, A. L., Zhmud, E. M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: random walks on groups; finite groups; group algebra; 20P05; 60B15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/814

Let \(P\) be a probability on a finite group \(G\), \(P^{(n)}=P \ast \ldots\ast P\) (\(n\) times) be an \(n\)-fold convolution of \(P\). If \(n \rightarrow \infty\), then under mild conditions \(P^{(n)}\) converges to the uniform probability \(U(g)=\frac 1{|G|}\) \((g\in G)\). We study the case when...