Buongiorno a tutti,

Vorremmo segnalarvi che venerdì prossimo (13 Dicembre) in aula 2BC30 (Torre Archimede, Università di Padova) ci saranno due seminari per il ciclo di seminari in Probabilità e Finanza di:

1) Pablo López Rivera (Université Paris Cité) https://www.ljll.fr/lopezrivera/ https://www.ljll.fr/lopezrivera/

Title: Functional inequalities in the discrete setting and the Poisson-Föllmer Process

Date: December 13, 2024, at 14:30, room 2BC30

Abstract: Functional inequalities are a ubiquitous tool in probability, since they help us quantify the convergence to equilibrium of ergodic Markov processes and imply good concentration properties. In the continuous setting, the Gaussian measure is a central object, since it satisfies both a Poincaré and a log-Sobolev inequality. In particular, Caffarelli's contraction theorem states that the optimal transport map pushing forward the Gaussian towards a measure which is more log-concave than it is 1-Lipschitz, a fact that allows us to extend these inequalities to those measures. Can we prove an analogous result in the discrete setting if we replace the Gaussian by the Poisson distribution? The type of measures that can arise as a pushforward of a discrete distribution is very limited; in addition, the lack of a chain rule in the discrete setting hinders the argument used in the continuous setting. In the first part of the talk, I will show how these obstacles can be overcome via a stochastic proof based on an entropy-minimizing process constructed by Klartag and Lehec, which we call the Poisson-Föllmer process. In the second part of the talk I will also use this process to give a stability result for Wu's log-Sobolev inequality, the Poissonan analog of the Gaussian one..

2) Nicolas Agote (Universidad de Buenos Aires)

Title: The potential method for community detection

Date: December 13, 2024, at 15:30, room 2BC30

Abstract: The Stochastic Block Model (SBM) is a random graph model where nodes are (randomly) partitioned into classes, or communities, which share a common label, and edges are (randomly) added between each pair of nodes depending on their community membership. It is a very popular model to study the community detection problem, where the aim is to predict the communities given a sample graph. In this talk we will explore the potential estimators, which exploit information obtained via random walks, specifically expected first visit times to some subset of revealed nodes, to predict the community structure. We will show that they allow for strongly consistent and efficient estimations, particularly for small subsets of nodes. This work has been done in collaboration with Inés Armendáriz (UBA), Pablo Ferrari (UBA), and Florencia Leonardi (USP).

Vi aspettiamo numerosi!

Alberto Chiarini e Alekos Cecchin

Sito web del seminario: https://www.math.unipd.it/~chiarini/seminars/