Densities of short uniform random walks in higher dimensions

Jonathan M. Borwein (1) , Armin Straub (2) , Christophe Vignat (3)

1 UoN - University of Newcastle [Australia]
2 University of South Alabama
3 L2S - Laboratoire des signaux et systèmes

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.

Domains: Mathematics [math]; Probability [math.PR]

Jonathan M. Borwein, Armin Straub, Christophe Vignat. Densities of short uniform random walks in higher dimensions. Journal of Mathematical Analysis and Applications, 2016, 437 (1), pp.668-707. ⟨10.1016/j.jmaa.2016.01.017⟩. ⟨hal-01261938⟩