[Todos] Seminario de Probabilidad y Estadística Matemática

[Pablo Groisman]

Seminario de Probabilidad y Estadística Matemática.

PROXIMO ENCUENTRO: Miércoles 13 de Julio 12:00hs.
EXPOSITOR: Roberto Fernández, Utrecht University
TITULO:  Regular g-measures are not always Gibbsian
LUGAR: Aula de Seminarios del Departamento de Matemática, 2do piso, Pabellón 1.

RESUMEN: Regular $g$-measures are discrete-time processes determined
by conditional expectations with respect to the past.  One-dimensional
Gibbs measures, on the other hand, are fields determined by
simultaneous conditioning on past and future.  For the Markovian and
exponentially continuous cases both theories are known to be
equivalent.  Its equivalence for more general cases was an open
problem.
We present a simple example settling this issue in a negative way:
there exist $g$-measures that are continuous and non-null but are not
Gibbsian.  Our example belongs, in fact, to a well-studied family of
processes with rather nice attributes:  It is a chain with
variable-length memory, characterized by the absence of phase
coexistence and the existence of a visible renewal scheme.

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