Logarithm laws for unipotent flows, I

Jayadev S. Athreya, Gregory A. Margulis

Research output: Contribution to journalArticlepeer-review


We prove analogs of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we obtain results for one parameter actions on the space of lattices SL(n, ℝ)/SL(n, ℤ). The key lemma for our results says the measure of the set of unimodular lattices in ℝn that does not intersect a 'large' volume subset of ℝn is 'small'. This can be considered as a 'random' analog of the classical Minkowski Theorem in the geometry of numbers.

Original languageEnglish (US)
Pages (from-to)359-378
Number of pages20
JournalJournal of Modern Dynamics
Issue number3
StatePublished - 2009
Externally publishedYes


  • Diophantine approximation
  • Geometry of numbers
  • Logarithm laws
  • Unipotent flows

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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