Short walk adventures

Abstract

We review recent development of short uniform random walks, with a focus on its connection to (zeta) Mahler measures and modular parametrisation of the density functions. Furthermore, we extend available "probabilistic" techniques to cover a variation of random walks and reduce some three-variable Mahler measures, which are conjectured to evaluate in terms of $L$-values of modular forms, to hypergeometric form.

15 pages

References in corpus (4)

• Elliptic integral evaluations of Bessel moments
• Wick rotations, Eichler integrals, and multi-loop Feynman diagrams
• A solution of Sun's $520 challenge concerning 520/pi
• A study of elliptic gamma function and allies

Cited by in corpus (3)

• Mahler measure numerology
• Hyper-Mahler measures via Goncharov-Deligne cyclotomy
• Ramanujan-type $1/\pi$-series from bimodular forms