Σεμινάριο Ανάλυσης και Πιθανοτήτων

Πότε 19/05/2017
από 01:10 έως 14:30
Που Αίθουσα Α32, Τμήμα Μαθηματικών
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Ομιλητής: Παύλος Τσατσούλης (University of Warwick).

Τίτλος: Spectral Gap for the Stochastic Quantisation Equation on the 2-dimensional Torus.



Περίληψη: We consider the stochastic quantisation equation on the 2-dimensional torus formally given by

 

where ξ is a space-time white noise, n is odd and .

In Constructive Quantum Field Theory the above equation was introduced to describe the dynamics of an infinite dimensional Gibbs measure on the space of Schwarz distributions (known as  the Euclidean Quantum Field Theory). It is already known that the equation admits a well-posed theory only as a renormalised problem (as it stands is ill-posed and it cannot be solved in any function space)
which provides Markov solutions evolving in a space of distributions of suitably negative regularity.

After a brief introduction on the topic, I will discuss recent results for the solutions of (1), including a strong dissipative bound independent of the initial condition and the strong Feller property for the associated Markov semigroup. I will then explain how, given a support theorem, these results imply exponential mixing (i.e exponential convergence to a unique invariant measure).

Joint work with H. Weber.