Dear all,

during May, prof. Mauro Mariani will be INdAM Visiting Professor at the University of Pisa, and will deliver a the first half of a PhD Course on

Long time asymptotic and criticality in random dynamics

(abstract below). The second half will be later given by Giacomo di Gesù (Sapienza Università di Roma). The format will be blended, in presence and online using Microsoft Teams. The first lecture is scheduled on

Thursday, May 5th, at 11 am,

at Aula Seminari of the Department of Mathematics (Largo Bruno Pontecorvo, 5, first floor)

and online at the link

https://teams.microsoft.com/l/meetup-join/19%3aNPe79QEwg0BQ31oFUsis6tD5qgF2b...

Dates and times later lectures are possibly subject to changes, but are now tentatively scheduled every Thursday and Friday, 11 am, same room (Aula Seminari), starting from Thursday 12th. No lecture will be delivered on Friday 6th.

Please feel free to forward this message to anyone who might be interested, and write me if you want to be added to the Team (to access records of the lectures and further material). Regards,

Dario Trevisan

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Abstract: The qualitative behavior of random evolutions in the long time asymptotic is a classical subject, which has recently found new motivations in high dimensional optimization. The course provides an introduction to classical and recent results concerning the long time behavior of some classes of Markov processes. In the first part, we will introduce some tools typical of potential theory in an elementary context, with focus on the reversibility non-reversibility paradigm. In the second part of the class, we will focus on establishing some recent results for more involved models and infinite-dimensional dynamics.

1. Ergodicity and long time behavior of Markov processes. 2. Potential theory and spectral analysis for processes on graphs. 3. Applications to statistical mechanics models.