Event Archive

Michael Aizenman - Studies of Critical Behavior Through Algorithmic Variance Bounds

Thursday, November 02, 2017 at 12:00pm - 01:00pm

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MATHEMATICAL PHYSICS SEMINAR
RUTGERS UNIVERSITY
HILL 705
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Michael Aizenman - Princeton University


  Date/Time/Location
Thursday, November 2nd, 12:00pm; Hill 705

Title
"Studies of Critical Behavior Through Algorithmic Variance Bounds "

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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