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arXiv · 0811.2806

Logarithm laws for unipotent flows, I

Jayadev S. Athreya·Grigorii Margulis
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Abstract

We prove analogues 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 $\R^n$ that does not intersect a `large' volume subset of $\R^n$ is `small'. This can be considered as a `random' analogue of the classical Minkowski theorem in the geometry of numbers.

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Jayadev S. Athreya, Grigorii Margulis. 2009-05-18. Logarithm laws for unipotent flows, I. https://arxiv.org/abs/0811.2806

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