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SUMMARY:Random graphs as models of quantum disorder
DTSTART:20260401T151500
DTEND:20260401T161500
DTSTAMP:20260404T113553Z
UID:7e461dce60bd0ded8865233c688fc9077ae2835cf8239e85a3e26f0c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Antti Knowles (Geneva)\nA disordered quantum system is mathema
 tically described by a large Hermitian random matrix. One of the most rema
 rkable phenomena expected to occur in such systems is a localization-deloc
 alization transition for the eigenvectors. Originally proposed in the 1950
 s to model conduction in semiconductors with random impurities\, the pheno
 menon is now recognized as a general feature of wave transport in disorder
 ed media\, and is one of the most influential ideas in modern condensed ma
 tter physics. A simple and natural model of such a system is given by the 
 adjacency matrix of a random graph. I report on recent progress in analysi
 ng the phase diagram for the Erdös-Renyi model of random graphs. In parti
 cular\, I explain the emergence of fully localized and fully delocalized p
 hases\, which are separated by a mobility edge. I also explain how to obta
 in optimal delocalization bounds using a new Bernoulli flow method. Based 
 on joint work with Johannes Alt\, Raphael Ducatez\, and Joscha Henheik.
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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