Archive ouverte HAL – When Random Walkers Help Solving Intriguing Integrals

Satya Majumdar 1 Emmanuel Trizac 1

Satya Majumdar, Emmanuel Trizac. When Random Walkers Help Solving Intriguing Integrals. Physical Review Letters, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.020201⟩. ⟨hal-02291790⟩

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.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques