*Tid:* **25 april 2016 kl 15.15-16.15.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedtsvägen 25, plan 7.
Karta!
*Föredragshållare:*
**
Takis Konstantopoulos
**
**Titel:**
Finite and infinite exchangeability
**Abstract**
Exchangeability is ubiquitous in probability theory, with applications
ranging from statistical mechanics to stochastic networks and bayesian
inference. The classical result in this area is de Finetti's theorem
that completely characterizes exchangeable probability measures on infinite
products of a "nice" space (e.g., a Polish space). But what happens
to exchangeable measures on finite products? It turns out that an analogous
result hold, but the mixing measure may not be positive.
We shall present a proof of this and show that no topological
assumptions are needed whatsoever. We also ask the question of whether
an exchangeable measure in n dimensions can be extended to n+1 or higher
dimensions. (This is not always the case, and this is a problem that appears,
e.g., in extensions of statistical physics models to higher dimensions).
We give a necessary and sufficient condition for this, but we do require
that the space be a locally compact Hausdorff space.
This is joint work with Svante Janson and Linglong Yuan.
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