Projecting the distribution of planar Browian motion at a stopping time through an analytic function

2016/06/10 by Greg Markowsky, Markowsky, Greg
Chemistry · Mathematics · Physics and Astronomy · #30A99 #60J65 #Analytic and geometric function theory #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1606.03186

openalex publication_date 2016/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A method is given of deriving the distribution of planar Brownian motion evaluated at certain stopping times using analytic functions. This method relies upon a generalization of the standard conformal invariance of harmonic measure. A number of examples are given, including several in which the stopping time in question is not the exit time of a domain. It is also shown how appropriate choices of domains and stopping times can lead to new proofs of identities, including Euler's Basel sum and a generalization of Leibniz's formula for π.

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