Random walks in Euclidean space

• Autores: Péter P. Varjú
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 181, Nº 1, 2015, págs. 243-301
• Idioma: inglés
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• Resumen

  • Fix a probability measure on the space of isometries of Euclidean space R d . Let Y 0 =0,Y 1 ,Y 2 ,�?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}}