Seminari di Probabilità, Pavia

Mercoledì 28 Febbraio 2018 nell'aula Beltrami del Dipartimento di Matematica dell' Università di Pavia (via Ferrata 1)

si svolgeranno due seminari:

Ore 14.30: Stephane Boucheron, Univ. Paris Diderot

"TBA"

Ore 15.30: Lorenzo Dello Schiavo, Universität Bonn

Characteristic functionals of Dirichlet measures and their algebraic properties

Abstract: We consider Dirichlet—Ferguson (DF) measures, a family of random probabilities on a locally compact Polish space X. Introduced by T. S. Ferguson in Ann. Stat. 1(2) 209ff., 1973, these measures have ever since found applications widely ranging from Bayesian non-parametrics to population genetics and stochastic dynamics of infinite particle systems. We compute the characteristic functionals of DF measures relying on those of their finite-dimensional marginalizations, the Dirichlet (D) distributions on standard simplices. In finite dimensions, we identify the dynamical symmetry algebra L of the characteristic functional of D as a simple Lie algebra of type A. Additionally, we show that all integer semi-lattices of certain posterior D distributions have a natural structure of weight Lie algebra module for L. A probabilistic interpretation and a partial generalization of these results to the infinite-dimensional case of DF measures is at hand. If time permits, we will also address a second characterization of DF measures by means of a Georgii—Nguyen—Zessin-type formula (joint work with E. W. Lytvynov, Swansea University).

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