20 Sep 2006; Mat-Nat Faculty (UiTø), room U1=A228. Wednesday 10:15-12:00

Martin Rypdal.

"Examples of phase transitions in countable state Markov chains".

It is a well known result of Ruelle that topological Markov chains over finite alphabets do not admit phase transitions. The result does not generalize to Markov chains over infinite (countable) alphabets, and examples of phase transitions have been provided by X. J. Wang, A.O. Lopez and O. Sarig.

In this lecture we will first discuss the notion of phase transition in a general context, before we review Sarig’s thermodynamic formalism for countable state Markov chains and present concrete examples of first order phase transitions.