Stochastic Analysis, Stochastic Partial Differential Equations and Applications to Fluid Dynamics and Particle Systems
timetable:
Mon 5 Jun, 15:25 - 15:55, Aula Mancini
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seminar: Gibbs measures on Brownian paths
speaker: Massimiliano Gubinelli (Université Paris Dauphine )abstract: We describe several results on existence and properties of Gibbs measures with respect to the Wiener measure which arise naturally when studying the ground state of a quantum particles interacting with scalar or vector boson fields. In the vector case, the energy in the Gibbs measure is given by a double stochastic integral. In the scalar case an additive renormalization could produce a double stochastic integral interaction term. In both cases, under suitable decay conditions, we can prove existence of the infinite volume limit. Finally, we discuss the problems linked to the characterization (à la DLR) of the infinite volume measure.
timetable:
Mon 5 Jun, 15:25 - 15:55, Aula Mancini
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