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SUMMARY:Random Schrödinger operator on fractals - Stanislav Molchanov (Un
 iversity of North Carolina)
DTSTART:20220228T140000Z
DTEND:20220228T150000Z
UID:TALK170210@talks.cam.ac.uk
DESCRIPTION:&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\
 ;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nb
 sp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;
 &nbsp\;&nbsp\;&nbsp\; Random Schr&ouml\;dinger operator on fractals\n&nbsp
 \;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&nbsp\;&n
 bsp\;&nbsp\;&nbsp\;&nbsp\; Stanislav Molchanov (UNC Charlotte\, USA\; HSE\
 , Moscow\, Russia)\n&nbsp\;\nThe talk will discuss two groups of localizat
 ion theorems. The first one concerns the Anderson model for graphs similar
  to the Sierpinski lattice. The spectral dimension of each graph is less t
 han 2 and &ndash\; in the spirit of the classical conjecture &ndash\; in t
 he wide class of random potentials\, the spectrum is pure point for an arb
 itrary small disorder. The theorems of the second group present localizati
 on results for continuous hierarchical Schr&ouml\;dinger operators. The ce
 ntral fact: for potentials of a certain class (finite rank random potentia
 ls)\, the spectrum is pure point in any dimension and arbitrary coupling c
 onstant.
LOCATION:Seminar Room 2\, Newton Institute
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