Mathematics

Findings from University of Rennes advance knowledge in mathematics

  2008 NOV 24 - (VerticalNews.com) -- According to recent research published in the Journal of Theoretical Probability, "l Let S be the multiplicative semigroup of q x q matrices with positive entries such that every row and every column contains a strictly positive element."

  "Denote by (X-n) n>= 1 a sequence of independent identically distributed random variables in S and by X-(n) = X-n...X-1, n>= 1, the associated left random walk on S. We assume that (Xn) n>= 1 satisfies the contraction property [GRAPHICS] where S is the subset of all matrices which have strictly positive entries," wrote H. Hennion and colleagues, University of Rennes.

  The researchers concluded: "We state conditions on the distribution of the random matrix X-1 which ensure that the logarithms of the entries, of the norm, and of the spectral radius of the products X-(n), n>= 1, are in the domain of attraction of a stable law."

  Hennion and colleagues published their study in the Journal of Theoretical Probability (Stable laws and products of positive random matrices. Journal of Theoretical Probability, 2008;21(4):966-981).

  For additional information, contact H. Hennion, University of Rennes, Institute Math Rennes, Campus Beaulieu, F-35042 Rennes, France.

  The publisher's contact information for the Journal of Theoretical Probability is: Springer, Plenum Publishers, 233 Spring St., New York, NY 10013, USA.

  Keywords: Mathematics, University of Rennes.

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