Memory loss near the boundary of null recurrence for Harris recurrent Markov chains and infinite measure preserving intermittent dynamical systems
Ergodic Theory and Dynamical Systems Seminar
21st November 2024, 2:00 pm – 3:00 pm
Fry Building, 2.04
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.
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