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SUMMARY:Victor Kleptsyn (Institute of Mathematical Research of Rennes)
DTSTART:20210224T150000Z
DTEND:20210224T160000Z
DTSTAMP:20260423T041509Z
UID:DSandPDEs/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DSandPDEs/9/
 ">The Furstenberg theorem : adding a parameter and removing the stationari
 ty (on a joint work with A. Gorodetski)</a>\nby Victor Kleptsyn (Institute
  of Mathematical Research of Rennes) as part of Dynamical systems and PDEs
 \n\n\nAbstract\nThe classical Furstenberg theorem describes the (almost su
 re) behaviour of a random product of independent matrices from SL(n\,R)\; 
 their norms turn out to grow exponentially. In our joint work\, we study w
 hat happens if the random matrices from SL(2\,R) depend on an additional p
 arameter. It turns out that in this new situation\, the conclusion changes
 . Namely\, under some natural conditions\, there almost surely exists a (r
 andom) "exceptional" set on parameters where the lower limit for the Lyapu
 nov exponent vanishes.\nAnother direction of the generalization of the cla
 ssical Furstenberg theorem is removing the stationarity assumption. That i
 s\, the matrices that are multiplied are still independent\, but no longer
  identically distributed. Though in this setting most of the standard tool
 s are no longer applicable (no more stationary measure\, no more Birkhoff 
 ergodic theorem\, etc.)\, it turns out that the Furstenberg theorem can (u
 nder the appropriate assumptions) still be generalized to this setting\, w
 ith a deterministic sequence replacing the Lyapunov exponent. These two ge
 neralizations can be mixed together\, providing the Anderson localization 
 conclusions for the non-stationary 1D random Schrodinger operators.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/9/
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