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SUMMARY:Antti Knowles (Université de Genève)
DTSTART:20201027T153000Z
DTEND:20201027T163000Z
DTSTAMP:20260423T005751Z
UID:OxfordRMT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OxfordRMT/4/
 ">Delocalization transition for critical Erdös-Rényi graphs</a>\nby Antt
 i Knowles (Université de Genève) as part of Oxford Random Matrix Theory 
 Seminars\n\n\nAbstract\nWe analyse the eigenvectors of the adjacency matri
 x of a critical Erdös-Rényi graph G(N\,d/N)\, where d is of order \\log 
 N. We show that its spectrum splits into two phases: a delocalized phase i
 n the middle of the spectrum\, where the eigenvectors are completely deloc
 alized\, and a semilocalized phase near the edges of the spectrum\, where 
 the eigenvectors are essentially localized on a small number of vertices. 
 In the semilocalized phase the mass of an eigenvector is concentrated in a
  small number of disjoint balls centred around resonant vertices\, in each
  of which it is a radial exponentially decaying function. The transition b
 etween the phases is sharp and is manifested in a discontinuity in the loc
 alization exponents of the eigenvectors. Joint work with Johannes Alt and 
 Raphael Ducatez.\n\nThis seminar will be held via zoom. Meeting link will 
 be sent to members of our mailing list (https://lists.maths.ox.ac.uk/mailm
 an/listinfo/random-matrix-theory-announce) in our weekly announcement on M
 onday.\n
LOCATION:https://researchseminars.org/talk/OxfordRMT/4/
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