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Local Limit Theorem in negative curvature
Ledrappier, Françoi...

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Local Limit Theorem in negative curvature by Ledrappier, François ( Author )
Lemonjar Open Access
N.A
13-03-2015
Consider the heat kernel p(t,x,y) on the universal cover X of a Riemannian manifold M of negative curvature. We show the local limit theorem for p : limt→∞t3/2eλ0tp(t,x,y)=C(x,y), where λ0 is the bottom of the spectrum of the geometric Laplacian and C(x,y) is a positive function which depends on x,y∈X. We also show that the λ0-Martin boundary of X is equal to its topological boundary. The Martin decomposition of C(x,y) gives a family of measures {μλ0x} on ∂M˜. We show that {μλ0x} is the unique family minimizing the energy or the Rayleigh quotient of Mohsen. We use the uniform Harnack inequality on the boundary ∂X and the uniform three-mixing of the geodesic flow on the unit tangent bundle SM for suitable Gibbs-Margulis measures.
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Article
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English
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MYR 0.00
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http://arxiv.org/abs/1503.04156
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