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DESCRIPTION: Let M_n be a uniformly-chosen random symmetric n x n matrix wi
th entries in {-1\,1}. What is the probability for det(M_n)=0? A wellknown
conjecture states that the probability of this event is asymptotically equa
l to the probability that two of the rows or columns of M_n are equal (up t
o a factor of +-1) and hence is equal to \Theta(n^2 2^{-n}). We developed
an inverse Littlewood-Offord theorem in Z^n_p that applies under very mild
conditions and made progress towards this conjecture\, showing that the pr
obability is bounded by exp(-c\sqrt{n}). Joint work with Marcelo Campos\,
Robert Morris and Natasha Morrison.
DTSTAMP:20211027T185800
DTSTART:20211101T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Letícia Mattos (Freie Universität Berlin): Singularity of random sy
mmetric matrices
UID:107919380@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20211101-C-Mattos.html
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