Pacific Dynamics Seminar: Sophie MacDonald

  • Date: 05/07/2020
  • Time: 14:00
Lecturer(s):
Sophie MacDonald, UBC
Location: 

Online

Topic: 

Factors of Gibbs measures on subshifts

Description: 

Classical results of Dobrushin and Lanford-Ruelle establish, in rough terms, that for a local energy function on a subshift without too much long-range order, the translation-invariant Gibbs measures are precisely the equilibrium measures. There are multiple definitions of a Gibbs measure in the literature, which do not always coincide. We will discuss two of these definitions, one introduced by Capocaccia and the other used by Dobrushin-Lanford-Ruelle, and outline a proof (available at [arxiv.org/abs/2003.05532]) that they are equivalent.

We will also discuss forthcoming work, in which we show that Gibbsianness is preserved by pushforward through a certain kind of almost invertible factor map. As an application in one dimension, we show that for a sufficiently regular potential, any equilibrium measure on an irreducible sofic shift is Gibbs. As far as we know, this is the first reasonably general result of the Lanford-Ruelle type for a class of subshifts without the topological Markov property.

Joint work with LuĂ­sa Borsato, with extensive advice from Brian Marcus and Tom Meyerovitch.

Other Information: 

For the Zoom Meeting ID and password, please contact the organizers at jathreya@uw.edu