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