Spectral gap properties for random walks on homogeneous spaces: examples and consequences
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About this item
| Description: |
Guivarch, Y (Université de Rennes 1)
Friday 04 July 2014, 11:30-12:20 |
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| Created: | 2014-07-15 10:36 |
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| Collection: | Interactions between Dynamics of Group Actions and Number Theory |
| Publisher: | Isaac Newton Institute |
| Copyright: | Guivarch, Y |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Co-authors: J.-P Conze, B. Bekka, E .LePage
Let E be a homogeneous space of a Lie group G, p a finitely supported probability measure on G, such that supp(p) generates topologically G. We show that, in various situations, convolution by p has a spectral gap on some suitable functional space on E . We consider in particular Hilbert spaces and Holder spaces on E and actions by affine transformations. If G is the motion group of Euclidean space V ,we get equidistribution of the random walk on V. If G is the affine group of V,p has a stationary probability, and the projection of p on GL(V) satisfies "generic" conditions we get that the random walk satisfies Frechet's extreme law , and Sullivan's Logarithm law. |
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