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SUMMARY:Continuity of Lyapunov Exponents via Large Deviations - Klein\, S\
 , Duarte\, P (Department of Mathematical Sciences\, NTNU)
DTSTART:20150402T113000Z
DTEND:20150402T123000Z
UID:TALK58725@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Large deviation type (LDT) estimates for transfer matrices are
  important tools in the study of discrete\, one dimensional\, quasi-period
 ic Schrodinger operators. They have been used to establish positivity of t
 he Lyapunov exponent\, continuity properties of the Lyapunov exponent and 
 of the integrated density of states\, estimates on the Green's function\, 
 Anderson localization.\n\nWe prove - in a general\, abstract setting - tha
 t the availability of appropriate LDT estimates implies continuity of the 
 Lyapunov exponents\, with a modulus of continuity depending explicitly on 
 the strength of the LDT.  The devil is of course in the details\, hidden h
 ere behind the words "availability" and "appropriate".\n\nWe show that the
  study of the Lyapunov exponents associated with a band lattice quasi-peri
 odic Schrodinger operator fits this abstract setting\, provided the potent
 ial is a real analytic function of (one or of) several variables and that 
 the frequency vector is Diophantine.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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