Dear colleagues,

it is our pleasure to invite you to the following online seminars (in two different days!)

Speaker: *Paolo Gibilisco* (Roma Tor Vergata) Title: *Information Geometry: an invitation to the basic results of the subject and to some new perspectives* Time: Monday, *April 19*, 5PM (Italian time)

Speaker: *Cambyses Rouzé *(Technische Universität München) Title: *Complete modified logarithmic Sobolev inequalities and quantum Gibbs samplers* Time: Tuesday, *April 20*, 5PM (Italian time)

Abstracts follow: one below in this message and one attached.

Zoom Link https://us02web.zoom.us/j/89543157111?pwd=NnAyblhVNkppeERRRFd1VGYwTkMyUT09 (the same for both seminars - ID and passcode below if necessary)

The seminars are a satellite activity of the PhD course "Introduction to coercive inequalities with applications in analysis and probability theory" (professor Boguslaw Zegarlinski - Imperial College, London)

Following speaker will be: *Giuseppe Savaré* on *April 22*nd, 4PM A specific announcement will be sent in the next days.

Best regards, Raffaella Carbone

*Cambyse Rouzé - Title and abstract*

Title: Complete modified logarithmic Sobolev inequalities and quantum Gibbs samplers

Abstract: Since the seminal works of Dobrushin-Shlosman and Stroock-Zegarlinski, equilibrium and out-of-equilibrium properties of classical lattice spin systems are known to be closely related: given a potential, one can construct a Markov process, called Glauber dynamics, whose reversing state coincides with the Gibbs state for the given potential. For these dynamics, Holley and Stroock made the key observation that systems thermalizing in times scaling logarithmically in the system size, a property known as rapid mixing, satisfy exponential decay of correlations at equilibrium. The converse implication, namely that exponential decay of correlations implies rapid mixing, was investigated later on in a series of articles by Zegarlinski and Stroock, who proved the stronger condition of an exponential entropic decay of the dynamics towards the limiting Gibbs measure, also known as logarithmic Sobolev inequality. In this talk, we will prove an extension of the result of Zegarlinski and Stroock to the quantum setting. More precisely, we will show that, given the Gibbs state $\sigma$ of a 2-local commuting Hamiltonian and above a critical temperature, there exists a local quantum Markovian evolution converging to $\sigma$ which satisfies the quantum modified logarithmic Sobolev inequality (MLSI) with a constant that does not depend on the size of the lattice. As a first step towards this proof, we will also provide a proof of the existence of the MLSI for finite dimensional systems coupled to an arbitrarily large, noiseless environment (also known as the complete MLSI constant), a problem that was left open until now.

This talk is based on the following papers: https://arxiv.org/abs/2009.11817 https://arxiv.org/abs/2102.04146

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Dottorato Matematica is inviting you to a scheduled Zoom meeting.

Topic: Seminars April 19 to 22 Time: Apr 19, 2021 05:00 PM Rome Apr 20, 2021 05:00 PM Apr 22, 2021 04:00 PM Please download and import the following iCalendar (.ics) files to your calendar system. Weekly: https://us02web.zoom.us/meeting/tZ0oc-qpqzwrG9W8L60lAyfp8kbqksDUWlwv/ics?ics...

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