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SUMMARY:Vishesh Jain (Stanford University)
DTSTART:20210419T190000Z
DTEND:20210419T200000Z
DTSTAMP:20260423T021345Z
UID:paw/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paw/29/">On 
 the real Davies' conjecture</a>\nby Vishesh Jain (Stanford University) as 
 part of Probability and Analysis Webinar\n\n\nAbstract\nWe show that every
  $n \\times n$ real matrix $A$ is within distance $\\delta \\|A\\|$ in the
  operator norm of an $n\\times n$ real matrix $A'$ whose eigenvectors have
  condition number $\\tilde{O}(\\text{poly}(n)/\\delta)$. In fact\, we show
  that with high probability\, an additive i.i.d. sub-Gaussian perturbation
  of $A$ has this property. Up to log factors\, this confirms a speculation
  of E.B. Davies. \n\nBased on joint work with Ashwin Sah (MIT) and Mehtaab
  Sawhney (MIT).\n
LOCATION:https://researchseminars.org/talk/paw/29/
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