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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A probabilistic proof of the fundamental theorem of algebra


Author: Mihai N. Pascu
Journal: Proc. Amer. Math. Soc. 133 (2005), 1707-1711
MSC (2000): Primary 30C15; Secondary 60J65
Published electronically: December 6, 2004
MathSciNet review: 2120250
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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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Additional Information

Mihai N. Pascu
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Address at time of publication: Faculty of Mathematics and Computer Science, “Transilvania” University of Braşov, Str. Iuliu Maniu Nr. 50, Braşov, Jud. Braşov – COD 2200, Romania
Email: pascu@math.purdue.edu, mihai.pascu@unitbv.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07700-7
PII: S 0002-9939(04)07700-7
Keywords: Brownian motion, L\'{e}vy's theorem, support theorem
Received by editor(s): October 10, 2003
Received by editor(s) in revised form: February 4, 2004
Published electronically: December 6, 2004
Additional Notes: This work was supported in part by NSF grant # 0203961 - DMS
Dedicated: I dedicate this paper to my dear friend M. K.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.