----------------------------------------------------------------------------- A v v i s o d i S e m i n a r i o ----------------------------------------------------------------------------- Venerdì 8 Maggio, ore 11 -----------------------------------------------------------------------------

Stanza 34 Dipartimento di Scienze Statistiche Sapienza Università di Roma

PROF. K.A. PENSON (Theoretical Physics, Sorbonne, Univ. Paris VI, France)

terrà un seminario dal titolo:

*PROBABILISTIC AND FREE-PROBABILISTIC PROPERTIES OF 2D CONSTELLATION NUMBERS*

*Abstract:* After a short introduction about the properties of classical Catalan numbers and their role in Physics we shall dwell on a certain quite vast generalisation of Catalan numbers called the constellation numbers. We solve exactly the Hausdorff moment problem for these numbers and provide explicit expressions for appropriate positive weight functions. For certain values of parameters we analyse the properties of these solutions from the point of view of the free probability, and demonstrate their infinite divisibility with respect to the free additive convolution. We introduce the idea of fractional constellation numbers and provide complete solutions to this particular case.

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Saluti Alessandro De Gregorio