When Random Walkers Help Solving Intriguing Integrals

Satya N. Majumdar and Emmanuel Trizac
Phys. Rev. Lett. 123, 020201 – Published 10 July 2019
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Abstract

We revisit a family of integrals that delude intuition and that recently appeared in mathematical literature in connection with computer algebra package verification. We show that the remarkable properties displayed by these integrals become transparent when formulated in the language of random walks. In turn, the random walk view naturally leads to a plethora of nontrivial generalizations that are worked out. Related complex identities are also derived, without the need of explicit calculation. The crux of our treatment lies in a causality argument where a message that travels at finite speed signals the existence of a boundary.

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  • Received 4 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.020201

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsStatistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Satya N. Majumdar and Emmanuel Trizac

  • LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

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Issue

Vol. 123, Iss. 2 — 12 July 2019

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