Todor Tsankov: On some generalizations of de Finetti’s theorem

19/July/2013, 13:30-15:00
Fields Institute, Room 210

Speaker:  Todor Tsankov

Title: On some generalizations of de Finetti’s theorem

Abstract:
A permutation group G acting on a countable set M is called

oligomorphic if the action of G on M^n has only finitely many orbits
for each n. Those groups are well known to model-theorists as
automorphism groups of omega-categorical structures. In this talk, I
will consider the question of classifying all probability measures on
[0, 1]^M invariant under the natural action of the group G. A number
of classical results in probability theory due to de Finetti,
Ryll-Nardzewski, Aldous, Hoover, Kallenberg, and others fit nicely
into this framework. I will describe a couple of new results in the
same spirit and a possible approach to carry out the classification in
general.

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