******************************************************************** SEMINARI DI PROBABILITÀ E STATISTICA MATEMATICA DIPARTIMENTO DI MATEMATICA "G. PEANO" UNIVERSITÀ DEGLI STUDI DI TORINO *********************************************************************

Martedì 15 Ottobre 2019 alle ore 16:30 in Sala S presso il Dipartimento di Matematica "G. Peano" dell'Università degli Studi di Torino, Via Carlo Alberto 10,

Il Prof. *Enrico Scalas* (Department of Mathematics – University of Sussex, UK)

terrà un seminario dal titolo

*Functional and Thermodynamic Limits of a Simple Coagulation-Fragmentation Markov Chain*

Abstract:

We discuss a simple random exchange model for the distribution of wealth. There are N agents, each one endowed with a fraction of the total wealth; indebtedness is not possible, so wealth fractions are positive random variables. At each step, two agent are randomly selected, their wealths are first merged (coagulation) and then randomly split into two parts (fragmentation) conserving the total wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we present its functional convergence to a continuous space - discrete time model. Then, we discuss how a continuous-time version of the one-point marginal Markov chain functionally converges to a kinetic equation of Boltzmann type. Solutions to this equation are presented and they coincide with the appropriate limits of the invariant measure for the marginal Markov chain. In this way, in this simple case, we complete Boltzmann’s program of deriving kinetic equations from random dynamics.

Joint work with: Bertram Duering, Nicos Georgiou, Sara Merino Aceituno

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