BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news326@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20181103T093011 DTSTART;TZID=Europe/Zurich:20181121T110000 SUMMARY:Seminar in probability theory: Antti Knowles (Geneva) DESCRIPTION:We consider the adjacency matrix of the Erdos-Renyi graph G(N\, p) in the supercritical regime pN > C log N for some universal constant C . We show that the eigenvalue density is with high probability well appr oximated by the semicircle law on all spectral scales larger than the typ ical eigenvalue spacing. We also show that all eigenvectors are completel y delocalized with high probability. Both results are optimal in the sens e that they are known to be false for pN < log N. A key ingredient of the proof is a new family of large deviation estimates for multilinear forms of sparse vectors. \\r\\nJoint work with Yukun He and Matteo Marcozzi. X-ALT-DESC: We consider the adjacency matrix of the Erdos-Renyi graph G(N\, p) in the supercritical regime pN >\; C log N for some universal consta nt C. We show that the eigenvalue density is with high probability well approximated by the semicircle law on all spectral scales larger than the typical eigenvalue spacing. We also show that all eigenvectors are compl etely delocalized with high probability. Both results are optimal in the sense that they are known to be false for pN <\; log N. A key ingredien t of the proof is a new family of large deviation estimates for multiline ar forms of sparse vectors. \nJoint work with Yukun He and Matteo Marcozz i. END:VEVENT END:VCALENDAR