JMD
Logarithm laws for unipotent flows, Ⅱ
Jayadev S. Athreya Gregory A. Margulis

We prove analogs of the logarithm laws of Sullivan and KleinbockMargulis in the context of unipotent flows. In particular, we prove results for horospherical actions on homogeneous spaces G/Γ.

keywords: Logarithm law unipotent flow norm-like pseudometric
JMD
Logarithm laws for unipotent flows, I
Jayadev S. Athreya Gregory A. Margulis
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 $\R^n$ that does not intersect a 'large' volume subset of $\R^n$ is 'small'. This can be considered as a 'random' analog of the classical Minkowski Theorem in the geometry of numbers.
keywords: Logarithm laws geometry of numbers. unipotent flows diophantine approximation

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