A central limit theorem for extremal characters of the infinite symmetric group

Jens Marklof előadásának absztraktja

(Joint with Andreas Strombergsson, Uppsala)

2013. március 14. csütörtök, 16:15

 
 

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are located at a random point field (such as a spatial Poisson process) or at the vertices of a Euclidean lattice. In the present paper we investigate quasicrystalline scatterer configurations, which are non-periodic, yet strongly correlated. A famous example is the vertex set of the Penrose tiling. Our main result is the existence of a limit distribution of 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. The key ingredients in the proofs are equidistribution theorems on homogeneous spaces, which follow from Ratner's measure classification.


 
Balázs Márton, 2013.03.07