Spectrum of non-Hermitian heavy tailed random matrices

Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some additional smoothness assumptions on the law of X_{jk}, we prove that there exists a deterministic sequence a_n ~ n^{1/alpha} and a probability measure mu_alpha on C depending only on alpha such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix a_n^{-1} (X_{jk})_{1<=j,k<=n} converges weakly to mu_alpha as n tends to infinity. Our approach combines Aldous & Steele's objective method with Girko's Hermitization using logarithmic potentials. The underlying limiting object is defined on a bipartized version of Aldous' Poisson Weighted Infinite Tree. Recursive relations on the tree provide some properties of mu_alpha. In contrast with the Hermitian case, we find that mu_alpha is not heavy tailed.Comment: Expanded version of a paper published in Communications in Mathematical Physics 307, 513-560 (2011

Prospection et valorisation du cépage Trousseau gris dans les Charentes

National audienceDe nos jours, le vignoble charentais est réputé pour ses eaux-de-vie de Cognac. La production de vins de bouche (vins de pays charentais), malgré une évolution importante (+ 117 % depuis quinze ans), reste marginale avec environ 122 000 hl en 2004. Pourtant avant le développement de la distillation au XVIIe siècle, les Charentes et particulièrement l’Aunis étaient réputées pour leurs vins. Le Trousseau gris, nommé « Chauché gris » en Charentes, constituait un élément important de l’encépagement

Polyelectrolyte multilayer films allow seeded human progenitor-derived endothelial cells to remain functional under shear stress in vitro

International audienceThere is considerable interest in making multilayer films for various applications, among which are cell contacting biomaterials, allowing new opportunities to prepare functionalized biomaterials. In this study we have explored the capability of poly(sodium-4-styrene sulfonate)/poly(allylamine hydrochloride) polyelectrolyte multilayer films (PMFs) as functional coatings for human progenitor-derived endothelial cells (PDECs), since the latter are a potential source of endothelial-type cells to be used in bioartificial vascular substitutes. We performed investigations with PDECs derived from peripheral blood and characterized as endothelial cells. After forming a confluent monolayer on PMFs they were exposed to laminar pulsatile physiological shear stress. We investigated whether PDECs were able to withstand shear stress and to respond at the mRNA (microarray analysis) and protein levels (thrombomodulin and tissue factor functional activity), in comparison with collagen I and fibrin glue used as controls. After shear stress the PDECs remained spread on the substrates, with a resulting increase in the number of expressed genes. Considering the functional significance of our findings for the regulation of coagulation and fibrinolytic factors, mRNA tissue plasminogen activator and thrombomodulin, profibrinolytic and thrombin inhibiting respectively, were overexpressed in PDECs after 6h shear stress. von Willebrand factor showed down-regulation, while tissue factor was up-regulated. We can speculate that PMFs could favour anti-thrombogenic activity by PDECs because activated protein C generation, measuring thrombomodulin activity, was particularly high on PMFs, but unchanged after 6h shear stress. Thus, PMFs could represent suitable coatings able to provide functional surfaces for endothelialization with PDECs