# Christophe Gallesco (UNICAMP)

In this talk, we will introduce the notions of dynamic uniqueness
and dynamic phase transition for chain of infinite oreder. We characterize
dynamic uniqueness/phase transition by proving several equivalent
conditions. In particular, we prove that dynamic uniqueness is equivalent
to convergence in total variation distance of all the chains starting from
different pasts. We also study the relationship between our definition of
uniqueness and the $\ell^2$ criteria for the uniqueness of $g$-measures.
We prove that the Bramson-Kalikow and  Hulse models exhibit dynamic
uniqueness if and only if the kernel is in $\ell^2$.
Finally, we prove that a $g$-measure $P$ is weak Bernoulli (or,
equivalently, $\beta$-mixing) if and only if $g$ exhibits dynamic
uniqueness for $P$-a.e. pasts, generalizing several results in the
literature.

Martes 24 de Noviembre, 17:00 hrs, Sala 5 facultad de matemáticas, Campus san Joaquín, PUC Chile.

##### Departamento de Matemáticas

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

##### Centro de Modelamiento Matemático (CMM)

Facultad de Ciencias Físicas y Matemáticas (FCFM)