One-sided versus two-sided regularity properties

Type: Groupe de travail probabilités
Site: UPEC
Auditorium, MSE
Date de début:
07/06/2022 - 14:00
Date de fin:
07/06/2022 - 16:00


Stochastic processes can be parametrised by time (such as occurs in Markov chains), in which case conditioning is one-sided (on the past), as naturally occurs in Dynamical Systems, or by one-dimensional space (which is the case, for example, for one-dimensional Markov fields), as is natural in Statistical Mechanics,  where the conditioning is two-sided (on the right and on the left).

I will discuss some examples, in particular generalising this distinction to g-measures versus Gibbs measures, where, instead of a Markovian dependence, the weaker property of continuity (in the product topology) is considered.

 In particular I will discuss when the two descriptions (one-sided or two-sided) produce the same objects and when they are different. We show moreover the role one-dimensional entropic repulsion plays in this setting. 

Based on joint work with R. Bissacot, E. Endo and A. Le Ny, and S. Shlosman.