Seminars & Colloquia Calendar
Studies of Critical Behavior Through Algorithmic Variance Bounds
Michael Aizenman, Princeton University
Location: HILL 705
Date & time: Thursday, 02 November 2017 at 12:00PM - 1:00PM
Abstract: It will be shown how the previous PDI-based proof of the sharpness of phase transition and mean-field critical exponent bound, established by D. Barky and the speaker for independent percolation (Q=1) and Ising spin systems (Q=2), can be rooted in the O’Donnell - Saks - Schramm - Servedio algorithmic variance inequality. The recent extension of this inequality to positively correlated variables, by Duminil-Copin - Raoufi - Tassion (DRT), allows to apply the PDI argument to all random cluster models (at Q>1). This approach allows a minor extension of the recent results of DRT concerning this class of models.
(Note: PDI = Partial Differential Inequalities.)