Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados

Optimal transport, concentration of measure and functional inequalities.

Event Date: Jun 16, 2015 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract: This talk is devoted to Talagrand’s transport-entropy inequalities and its deep connections to the concentration of measure phenomenon, large deviation theory and logarithmic Sobolev inequalities. After an introductive part on the field, I will present recent results obtained with P-M Samson and C. Roberto characterizing different functional inequalities in terms of concentration of measure properties. If time enables, I will also present some works in progress about transport inequalities in a discrete setting.

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Quenched Voronoi percolation

Event Date: Jan 13, 2015 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

  Resumen:  In a seminal work from 1999, Benjamini, Kalai and Schramm introduced a framework for studying sensitivity of Boolean functions with respect to small portions of noise. They moreover made a series of conjectures that have been highly influential for the development since. We will in this talk discuss the solution to one of these conjectures, concerning Voronoi percolation: Position a large number of points in the unit square and consider their Voronoi tessellation. Next, colour each cell either red or blue. The question is whether from observing the tessellation, but not the...

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