A probabilistic proof of the fundamental theorem of algebra

Pascu, Mihai

doi:10.1090/S0002-9939-04-07700-7

A probabilistic proof of the fundamental theorem of algebra
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by Mihai N. Pascu PDF

Proc. Amer. Math. Soc. 133 (2005), 1707-1711 Request permission

Abstract:

We use Lévy’s theorem on invariance of planar Brownian motion under conformal maps and the support theorem for Brownian motion to show that the range of a non-constant polynomial of a complex variable consists of the whole complex plane. In particular, we obtain a probabilistic proof of the fundamental theorem of algebra.

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