Geodesic
Random walks in Euclidean space
Péter Pál Varjú1
1 Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB, England and Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Annals of mathematics, Tome 181 (2015) no. 1, pp. 243-301.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Fix a probability measure on the space of isometries of Euclidean space $\mathbf{R}^d$. Let $Y_0=0,Y_1,Y_2,\ldots\in\mathbf{R}^d$ be a sequence of random points such that $Y_{l+1}$ is the image of $Y_l$ under a random isometry of the previously fixed probability law, which is independent of $Y_l$. We prove a Local Limit Theorem for $Y_l$ under necessary nondegeneracy conditions. Moreover, under more restrictive but still general conditions we give a quantitative estimate which describes the behavior of the law of $Y_l$ on scales $e^{-cl^{1/4}}$.="" ="" l^{1="" p=""> \lt>
DOI : 10.4007/annals.2015.181.1.4

Péter Pál Varjú 1

1 Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB, England and Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel 
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Péter Pál Varjú. Random walks in Euclidean space. Annals of mathematics, Tome 181 (2015) no. 1, pp. 243-301. doi : 10.4007/annals.2015.181.1.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2015.181.1.4/

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