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Démonstration probabiliste du théorème de d’Alembert. (French) Zbl 0558.60012

Sémin. de probabilités XIX, Univ. Strasbourg 1983/84, Proc., Lect. Notes Math. 1123, 207-208 (1985).
[For the entire collection see Zbl 0549.00007.]
B. Davis [Trans. Am. Math. Soc. 213, 353-362 (1975; Zbl 0292.60126)] proved the Picard’s theorem using the Brownian motion in the complex domain. In this paper the author gives a one page proof for the fundamental theorem of algebra by using the well known properties of the Brownian motion in the complex domain.

MSC:

60B99 Probability theory on algebraic and topological structures
60J65 Brownian motion
58J65 Diffusion processes and stochastic analysis on manifolds
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