[Combprob] talk by Van Vu this Thursday: " Random matrices have simple spectrum"

[Daniel Spielman]

at 4pm in LOM 215

 Random matrices have simple spectrum

A symmetric matrix has  simple spectrum if all eigenvalues are different.
In 1980s, Babai conjectured that random graphs have simple spectrum with
probability tending to 1.

Confirming this conjecture, we   prove the simple spectrum property  for a
large class of random matrices.
If time allows, we will  discuss the harder problem of bounding the
spacings between consecutive eigenvalues, with motivation from mathematical
physics and numerical linear algebra.

Several open questions will also be presented.

https://urldefense.proofpoint.com/v2/url?u=https-3A__sites.google.com_a_yale.edu_combprob_home&d=AwIBaQ&c=-dg2m7zWuuDZ0MUcV7Sdqw&r=LF0MQT9lkPQlp3gHlW9D2fTc0d4apDhCuC758tavUvQ&m=70nXfA5dgf7zMaP4P7ggHIazFAC86rTQd-ltnJPIGeg&s=SF3Vfi8LU5WqDJwkwwttLzPu54PwWHHv4pwXrqzmAmA&e= 
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