Mathematics

Research from P. Bourgade and co-authors reveals new findings on science

  2008 NOV 24 - (VerticalNews.com) -- "In this article, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix," scientists in Paris, France report.

  "We recover the Mellin-Fourier transform of such a random polynomial, first obtained by Keating and Snaith in [8] using a simple recursion formula, and from there we are able to obtain the joint law of its radial and angular parts in the complex plane. In particular, we show that the real and imaginary parts of the logarithm of the characteristic polynomial of a random unitary matrix can be represented in law as the sum of independent random variables," wrote P. Bourgade and colleagues.

  The researchers concluded: "From such representations, the celebrated limit theorem obtained by Keating and Snaith in [8] is now obtained from the classical central limit theorems of probability theory, as well as some new estimates for the rate of convergence and law of the iterated logarithm-type results."

  Bourgade and colleagues published their study in Duke Mathematical Journal (The characteristic polynomial of a random unitary matrix: A probabilistic approach. Duke Mathematical Journal, 2008;145(1):45-69).

  For more information, contact P. Bourgade, Ecole National Super Telecommun Bretagne, F-75634 Paris 13, France.

  Publisher contact information for the Duke Mathematical Journal is: Duke University Press, 905 W Main St., Ste. 18-B, Durham, NC 27701, USA.

  Keywords: Central Limit Theorem, Mathematics, Polynomial.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.