[math-ias] Time and location Change: Non-equilibrium Dynamics and Random Matrices -- Thursday, September 26

[Anthony V. Pulido]

Thursday, September 26

Non-equilibrium Dynamics and Random Matrices
Topic:         Kinetic transport in quasicrystals
Speaker:     Jens Marklof, University of Bristol
Time/Room:     11:00am - 12:00pm/West Bldg. Lect. Hall
Abstract:    See below

3 Kinetic transport in quasicrystals
   Jens Marklof

Previous studies of kinetic transport in the Lorentz gas have been limited 
to cases where the scatterers are distributed at random (e.g. at the points 
of a spatial Poisson process) or at the vertices of a Euclidean lattice. In 
this talk I will report on recent joint work with Andreas Strombergsson 
(Uppsala) on quasicrystalline scatterer configurations, which are 
non-periodic, yet strongly correlated. A famous example is the vertex set 
of the Penrose tiling. Our main result proves the existence of a limit 
distribution for the free path length, which answers a question of 
Wennberg. The limit distribution is characterised by a certain random 
variable on the space of higher dimensional lattices, and is distinctly 
different from the exponential distribution observed in the random setting. 
I will also discuss related results for other aperiodic scatterer 
configurations, such as the union of pairwise incommensurate lattices. The 
key ingredients in the proofs are equidistribution theorems on homogeneous 
spaces, which follow from Ratner's measure classification theorem.
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