Circular Law Theorem for Random Markov Matrices

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum. In particular, when X11 follows an exponential law, then M belongs to the Dirichlet Markov Ensemble of random stochastic matrices. Our main result states that with probability one, the counting probability measure of the complex spectrum of n^(1/2)M converges weakly as n tends to infinity to the uniform law on the centered disk of radius sigma/m. The bounded density assumption is purely technical and comes from the way we control the operator norm of the resolvent.Comment: technical update via http://HAL.archives-ouvertes.f

Un essai de Cours de perfectionnement

Aubrun Ph. Un essai de Cours de perfectionnement. In: La revue pédagogique, tome 75, Juillet-Décembre 1919. pp. 34-41

Un essai de Cours de perfectionnement

Aubrun Ph. Un essai de Cours de perfectionnement. In: La revue pédagogique, tome 75, Juillet-Décembre 1919. pp. 34-41

Experimental lift control using fluidic jets on a model wind turbine

International audienc

Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet

International audienc

Corrosion of plain tinplate cans by light coloured fruits in syrup

17.50; Translated from French (Bull. Cent, Rech. Fer-Blanc 1985-86 p. 5-10)Available from British Library Document Supply Centre- DSC:9022.06(BISI-Trans--26952)T / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo