Short walk adventures

Armin Straub; Wadim Zudilin

doi:10.1007/978-3-030-36568-4_27

Short walk adventures

Number Theory 2020-03-19 v2 Mathematical Physics Classical Analysis and ODEs K-Theory and Homology math.MP Probability

Authors: Armin Straub , Wadim Zudilin

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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.

Keywords

random walk in random environment

Cite

@article{arxiv.1801.06002,
  title  = {Short walk adventures},
  author = {Armin Straub and Wadim Zudilin},
  journal= {arXiv preprint arXiv:1801.06002},
  year   = {2020}
}