题目： Memory loss near the boundary of null recurrence for Harris recurrent Markov chains and intermittent dynamical systems

报告人：Alexey Korepanov（Loughborough University）

时间: 2024年11月29日（周五），14:00-15:00

地点: 纯水楼301

摘要:  Memory loss is a quantification of how quickly an evolving system forgets its initial state. For example, for a Markov chain with transition operator P, given two probability measures mu and nu, we may want to know how quickly the distance between P^n mu and P^n nu decays in total variation. For Markov chains with slow (polynomial) recurrence, memory loss has been very well understood half a century ago (starting with Orey or Pitman) as long the chain is positive recurrent, yet we could not find any results in the null recurrent case (even though related questions are a subject of well developed Renewal Theory). A similar situation takes place in chaotic dynamical systems. I'll present (first?) results on memory loss that work for positive as well as null recurrent systems, taking a particular interest in proofs that survive the transition between positive and null recurrence. This is a joint work in progress with Ilya Chevyrev.

邀请人：陈剑宇