[CvGmt News] [cvgmt seminar] The low temperature limit of Dirichlet energies

[matteo.novaga at unipi.it]

The low temperature limit of Dirichlet energies
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http://cvgmt.sns.it/seminar/670/

Date: Monday, Dec 17, 2018

Time: 10:30

Place: Aula Marie Curie, Scuola Normale Superiore

Speaker: Mauro Mariani  (High School of Economics, Moscow)



Abstract. Let $M$ be a Riemannian manifold equipped with a reference measure $m$ with density $\exp(- V/T)$  with respect to the volume measure, where $V$ represents a potential and the positive constant $T$ represents the temperature. The Dirichlet energy with reference measure m is a classical functional defined on the space of probability measures on $M$. I will discuss the variational convergence of such a functional in the limit $T \to 0$. In particular, if $V$ is not convex, a non-trivial expansion by $\Gamma$-convergence holds under generic hypotheses on $V$. 
The results are based on a joint work with G. DiGesu (TU Wien).