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Mathematical Physics Seminar

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.)


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