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Regular version of the site

Book chapter

The Brownian motion on Aff(R) and quasi-local theorems

P. 97-124.

This paper is concerned with Random walk approximations of the
Brownian motion on the Affine group Aff(R). We are in particular interested
in the case where the innovations are discrete. In this framework, the return
probabilities of the walk have fractional exponential decay in large time, as
opposed to the polynomial one of the continuous object. We prove that in
tegrating those return probabilities on a suitable neighborhood of the origin,
the expected polynomial decay is restored. This is what we call a Quasi-local
theorem.








In book

Canzani Y., Chen L., Jakobson D. Vol. 739: Probabilistic Methods in Geometry, Topology and Spectral Theory. AMS, 2019.