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# Short walk adventures (in memory of Jon Borwein)

Short walk adventures (in memory of Jon Borwein)
Armin Straub, Wadim ZudilinSpringer Proceedings in Mathematics & Statistics — From Analysis to Visualization: JBCC 2017 — Volume 313, 2020, Pages 423-439

## 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.

@article{zmahler-jon-2020,
}