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Mercoledì 26 febbraio alle ore 14.00, nell'ambito dei Junior Seminars dei dottorandi di Matematica, Mario Morellini (dottorando, Università degli Studi Roma Tre) terrà il seminario dal titolo "Nonlinear Spin System".
Abstract: In this seminar, we explore a class of nonlinear dynamics governed by the framework of mass action dynamics, which models the evolution of systems through pairwise interactions. This framework underpins several important nonlinear models across disciplines, including chemical reaction networks, Boltzmann’s ideal gas model, and recombination processes in population genetics and genetic algorithms.
Our primary focus is on the nonlinear dynamics of spin systems, with an emphasis on the Ising model. Specifically, we investigate the convergence to equilibrium for spin systems at high temperatures, where non-trivial correlations are present.
Utilizing Kac’s Program, we interpret these nonlinear systems as limits of Markov chain particle systems under the propagation of chaos as system size tends to infinity. This perspective enables us to estimate the rate of convergence to equilibrium. A key aspect of our approach is ensuring that the Modified Log-Sobolev inequalities used to study the particle systems remain independent of system size. When this condition is met, the nonlinear system converges to equilibrium at the same rate as its corresponding particle system.
We will present two methods for analyzing this convergence: 1. A direct approach using McKean trees to study the nonlinear system. 2. An indirect approach that derives convergence from particle systems using size-independent Modified Log-Sobolev inequalities.
Il seminario è organizzato dai dottorandi di Matematica e si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, via della Vasca Navale 84, aula A.
