5 сентября, вторник, 14:00, ауд. 307 (ОБРАТИТЕ ВНИМАНИЕ на нестандартное время).
Aernout van Enter (Uni Groningen)
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 genralisation 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.
This is a joint work with R.Bissacot, E.Endo and A. Le Ny.
| 31.08.2017 | |