Stationary measures and invariant subsets of homogeneous spaces (II)

By Y. Benoist, Jean-François Quint. 2013

92 citations recorded by the source corpus.

Let G be a real Lie group, be a lattice in G and be a compactly generated closed subgroup of G. If the Zariski closure of the group Ad() is semisimple with no compact factor, we prove that every -orbit closure in G= is a nite volume homogeneous space. We also establish related equidistribution properties.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4d0007d7df41938e19bbf37c50f481232b45a9a1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Jon Chaika
2. A. Eskin
3. Jean-François Quint
4. Y. Benoist
5. Harald Andrés Helfgott
6. Jayadev S. Athreya

In Mathematical Physics

1. Jean-François Quint
2. Y. Benoist
3. Jon Chaika
4. A. Eskin
5. Dawei Chen
6. Maryam Mirzakhani
7. Don Zagier
8. A. Zorich

Citations in the corpus

• Every flat surface is Birkhoff and Oseledets generic in almost every direction (2013, methodology): “Let Ube an open subset of M. Then, for µN-almost all g¯ ∈ SL(2,R)N, we have lim N→∞ 1 N XN n=1 χU(gn ...g1x) = νM(U), where νM is the affine measure whose support is M. Our proof of Theorem 2.1 follows [BQ]. Let x, M and νM be as in Theorem 2.1. We begin with the following: Lemma 2.3. For every x, alm”
• Stationary measures and invariant subsets of homogeneous spaces (III) (2013, methodology): “4, this set plays a key role in the proofs, since, according to the main result of [4], every Γ-invariant Γ-ergodic probability measure on X is equal to νY for some Y in SX(Γ).”
• Random Walks on Reductive Groups (2016, methodology): “Indeed this version, which adapts Breuillard’s LLT for sums of iid real numbers in [30], is the one which is needed in [15].”