Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
3 place Victor Hugo
Case 19
13331 Marseille Cedex 3


Regular samplers and the De Finetti construction in Integrable Cones

Date(s) : 30/05/2024   iCal
11h00 - 12h30

The starting point of this talk is the structure of the object
!Bool in probabilistic coherent spaces. For the purpose of building a
semantics interpretation for PCF_proba, it is enough to consider elements of
!Bool that are promotions of elements in Bool, but !Bool contains also
more exotic elements, that can nonetheless be seen as probabilistic samplers
(in the sense that they can handle any number of query from a program !Bool → σ
to its argument, seen as a random oracle). In this work, we present a
caracterisation of all total elements in !Bool: we show that they can all be
seen as continuous mixture of promotions. The central element of this proof
is an extension to the category of integrable cones of the categorical
version[1] of the De Finetti theorem (that says that there is a one-to-one
correspondance between the continuous probability distributions on [0,1], and
the infinite exchangeable sequence of discrete random variables on booleans).

[1] B. Jacobs and S. Staton. De finetti’s construction as a categorical limit, CMCS 2020.

Site Sud, Luminy, TPR2, Salle de Séminaire 304-306 (3ème étage)


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