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Семинар Добрушинской лаборатории Высшей школы современной математики МФТИ



Onesided versus twosided points of view Aernout van Enter^{} ^{} Uni Groningen 

Аннотация: Abstract: Finitestate, discretetime Markov chains coincide with Markov fields on Z, (which are nearestneighbour Gibbs measures in one dimension). That is, the onesided Markov property and the twosided 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 onesided Markov measures leads to the socalled "gmeasures" (aka "chains with complete connection", "uniform martingales",..), whereas the twosided genralisation leads to the class of Gibbs or DLR measures, as studied in statistical mechanics. It was known before that there exist gmeasures 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 longrange, Dyson model, Gibbs measures. This is a joint work with R.Bissacot, E.Endo and A. Le Ny. Язык доклада: английский 