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Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature

Marc ArnaudonThomas Simon — 2005

Annales de l’institut Fourier

We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle, and one of us . Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one space parameter...

Small ball probabilities for stable convolutions

Frank AurzadaThomas Simon — 2007

ESAIM: Probability and Statistics

We investigate the small deviations under various norms for stable processes defined by the convolution of a smooth function f : ] 0 , + [ with a real Lévy process. We show that the small ball exponent is uniquely determined by the norm and by the behaviour of at zero, which extends the results of Lifshits and Simon, (2005) 725–752 where this was proved for being a power function (Riemann-Liouville processes). In the Gaussian case, the same generality as Lifshits and Simon, ...

A descriptive view of unitary group representations

Simon Thomas — 2015

Journal of the European Mathematical Society

In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if G and H are countable amenable non-type I groups, then the unitary duals of G and H are Borel isomorphic.

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