### One-sided versus two-sided regularity properties

Ergodic Theory and Dynamical Systems Seminar

17th March 2022, 2:00 pm – 3:00 pm

Fry Building, 2.04

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.

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