Abstract : We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our surprise, we are able to provide complete extensions to arbitrary dimensions for most of the central results known in the two-dimensional case.
Type de document :
Article dans une revue
Journal of Mathematical Analysis and applications, Elsevier, 2016, 437 (1), pp.668-707 〈10.1016/j.jmaa.2016.01.017 〉
https://hal-centralesupelec.archives-ouvertes.fr/hal-01261938
Contributeur : Christophe Vignat
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Soumis le : mardi 26 janvier 2016 - 05:54:52
Dernière modification le : mercredi 18 avril 2018 - 20:02:04
Jonathan M. Borwein, Armin Straub, Christophe Vignat. Densities of short uniform random walks in higher dimensions. Journal of Mathematical Analysis and applications, Elsevier, 2016, 437 (1), pp.668-707 〈10.1016/j.jmaa.2016.01.017 〉. 〈hal-01261938〉
