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Research Bernoulli Institute Calendar Colloquia - Mathematics

Colloquium Mathematics, Prof. Dr. A.C.D. van Enter

When:Tu 25-04-2017 11:30 - 12:30

T itle: One-sided versus two-sided points  of view


Finite-state,discrete-time Markov chains coincide with Markov fields on Z, (which are  nearest-neighbour  Gibbs measures in one dimension). That is, the one-sided Markov property and the two-sided Markov property are equivalent.

We discuss to what extent this remains true if we try to weaken the Markov property to the almost Markov property, which is a form of continuity of conditional probabilities. The generalisation of the one-sided Markov measures leads to the so-called "g-measures" (aka "chains with complete connection", "uniform martingales",..), whereas the two-sided generalisation leads to the class of Gibbs or DLR measures, as studied in statistical mechanics. It was known before that there exist
g-measures which are not Gibbs measures.  It is shown here that neither class includes the other.
We consider  this issue  in particular on the example of  long-range, Dyson model, Gibbs measures.

(Work with R.Bissacot,E.Endo and A. Le Ny).

Colloquium coordinators are Prof.dr. A.J. van der Schaft ( a.j.van.der.schaft )

Dr. A.V. Kiselev (e-mail: a.v.kiselev )