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Localization and Delocalization in Erdös-Rényi Graphs

[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 2 September 20, 2021 - September 24, 2021

September 24, 2021 (11:10 AM PDT - 12:00 PM PDT)
Speaker(s): Antti Knowles (University of Geneva)
Location: MSRI: Simons Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Abstract

The Erdös-Renyi graph G(N,d/N) is well known to undergo a dramatic change of behaviour around d of order log N. Below this threshold the graph develops inhomogeneities, which result in the emergence of a localized phase, in coexistence with a delocalized phase. I give an overview of the corresponding phase diagram, along with recent progress in establishing it rigorously. Joint work with Johannes Alt and Raphael Ducatez.

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