A probabilistic proof of the Open Mapping Theorem for analytic functions

TL;DR

This paper provides a concise proof of the Open Mapping Theorem for analytic functions using the conformal invariance property of Brownian motion, connecting probability theory with complex analysis.

Contribution

It introduces a probabilistic approach to prove the Open Mapping Theorem, offering an alternative to traditional complex analysis methods.

Findings

Probabilistic proof leverages Brownian motion invariance

Simplifies understanding of the Open Mapping Theorem

Bridges stochastic processes with complex analysis

Abstract

The conformal invariance of Brownian motion is used to give a short proof of the Open Mapping Theorem for analytic functions.