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Spherical averages in the space of marked lattices

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)75-102
Number of pages28
JournalGeometriae Dedicata
Volume186
Issue number1
Early online date28 Jun 2016
DOIs
DateAccepted/In press - 17 Jun 2016
DateE-pub ahead of print - 28 Jun 2016
DatePublished (current) - Feb 2017

Abstract

A marked lattice is a d-dimensional Euclidean lattice, where each lattice point is
assigned a mark via a given random field on Zd. We prove that, if the field is strongly mixing with a faster-than-logarithmic 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 non-trivial 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 Boltzmann-Grad limit.

    Research areas

  • Equidistribution, Homogeneous dynamics, Lorentz gas, Measure rigidity, Random process

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at http://link.springer.com/article/10.1007/s10711-016-0180-2. Please refer to any applicable terms of use of the publisher.

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