Random Walks on Semigroups and the Tsetlin Library and other Markov Chains
Random walks on groups have been studied for many years. The corresponding theory on semigroups has lain dormant until the past 15 years, when it was realized that a number of important Markov chains were modeled by random walks on semigroups. These include the Tsetlin library and related models.
The class of semigroups that arise has the property that all of their representations by matrices are triangularizable and have eignvalues either 0 or 1. This allows for the use of representation theoretic methods to rapidly gain information on the corresponding Markov chain.
No previous knowledge of semigroup theory nor of representation theoretic methods in probability are assumed for the talk.
תאריך עדכון אחרון : 18/04/2012