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On a multi-scale refinement of the 2nd moment method

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Co-authors: Louis-Pierre Arguin (University of Montreal), David Belius (University of Montreal ), Anton Bovier (University of Bonn)

The 2nd moment method is a powerful tool in the analysis of the extremes of random combinatorial structures. I will present a multi-scale refinement of the method which is based on a coarse-graining scheme; this is inspired by the picture which has recently emerged in the study of the extremes of branching Brownian motion [Arguin-Bovier-Kistler ‘13 / Aidekon-Beresticky-Brunet-Shi ‘13]. The refinement can also be applied to the study of the extremes of the 2dim Gaussian free field [Bolthausen-Deuschel-Giacomin ‘00 /Bramson-Ding-Zeitouni ‘13 / Biskup-Louidor ‘13], and allows to derive sharp estimates on 2dim cover times [Belius-Kistler ‘14]. Time permitting, I will also discuss a procedure of local projections which seemingly identifies scales from “first principles”; this may be useful to rigorously address certain conjectures [Fyodorov-Hiary-Keating ‘12] concerning the extremes of the Riemann zeta function along the critical line, or the extremes of the characteristic polynomials of CUE random matrices.

This talk is part of the Isaac Newton Institute Seminar Series series.

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