Abstract
A marked lattice is a ddimensional Euclidean lattice, where each lattice point is
assigned a mark via a given random field on Z^{d}. We prove that, if the field is strongly mixing with a fasterthanlogarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a nontrivial fiber bundle over such a space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the BoltzmannGrad limit.
assigned a mark via a given random field on Z^{d}. We prove that, if the field is strongly mixing with a fasterthanlogarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a nontrivial fiber bundle over such a space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the BoltzmannGrad limit.
Original language  English 

Pages (fromto)  75102 
Number of pages  28 
Journal  Geometriae Dedicata 
Volume  186 
Issue number  1 
Early online date  28 Jun 2016 
DOIs  
Publication status  Published  Feb 2017 
Keywords
 Equidistribution
 Homogeneous dynamics
 Lorentz gas
 Measure rigidity
 Random process
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Professor Jens Marklof
 Science Faculty Office  Dean of the Faculty of Science and Professor of Mathematical Physics
 Probability, Analysis and Dynamics
 Pure Mathematics
 Ergodic theory and dynamical systems
Person: Academic , Member