Skip to content

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
Issue number1
Early online date28 Jun 2016
DateAccepted/In press - 17 Jun 2016
DateE-pub ahead of print - 28 Jun 2016
DatePublished (current) - Feb 2017


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

Download statistics

No data available



  • Full-text PDF (final published version)

    Rights statement: This is the final published version of the article (version of record). It first appeared online via Springer at Please refer to any applicable terms of use of the publisher.

    Final published version, 649 KB, PDF document

    Licence: CC BY


View research connections

Related faculties, schools or groups