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SUMMARY:Peter Hislop (University of Kentucky)
DTSTART:20211220T151500Z
DTEND:20211220T161500Z
DTSTAMP:20260423T052641Z
UID:MAS-MP/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAS-MP/37/">
 Random band matrices in the localization regime</a>\nby Peter Hislop (Univ
 ersity of Kentucky) as part of Munich-Copenhagen-Santiago Mathematical Phy
 sics seminar\n\n\nAbstract\nThe problem of determining the local eigenvalu
 e statistics (LES) for one-dimensional random band matrices (RBM) will be 
 discussed with an emphasis on the localization regime. RBM are real symmet
 ric $(2N+1)\\times(2N+1)$ matrices with nonzero entries in a band of width
  $2N\\alpha+1$ about the diagonal\, for $0\\leq \\alpha \\leq 1$. The nonz
 ero entries are independent\, identically distributed random variables. It
  is conjectured that as $N\\rightarrow \\infty$ and for $0\\leq \\alpha <\
 \frac{1}{2}$\, the LES is a Poisson point process\, whereas for $\\frac{1}
 {2}<α≤1$\, the LES is the same as that for the Gaussian Orthogonal Ense
 mble. This corresponds to a phase transition from a localized to a delocal
 ized state as α passes through $\\frac{1}{2}$. In recent works with B. Br
 odie and with M. Krishna\, we have made progress in proving this conjectur
 e for $0\\leq \\alpha <\\frac{1}{2}$.\nSome of the results by others for t
 he delocalized state with $\\frac{1}{2}<\\alpha≤1$\nwill also be describ
 ed.\n
LOCATION:https://researchseminars.org/talk/MAS-MP/37/
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