Some new estimates on the spectral shift function associated with random Schr\"{o}dinger operators

We prove some new pointwise-in-energy bounds on the expectations of various spectral shift functions associated with random Schr\"{o}dinger operators in the continuum having Anderson-type random potentials in both finite-volume and infinite-volume. These estimates are a consequence of our new Wegner estimate for finite-volume random Schr\"{o}dinger operators. For lattice models, we also obtain a representation of the infinite-volume density of states in terms of a spectral shift function. For continuum models, the corresponding measure is absolutely continuous with respect to the density of states and agrees with it in certain cases. We present a variant of a new spectral averaging result and use it to prove a pointwise upper bound on the SSF for finite-rank perturbations.Comment: Some results were improved and some proofs simplifie

Lifshitz tails estimate for the density of states of the Anderson model

We prove an upper bound for the (differentiated) density of states of the Anderson model at the bottom of the spectrum. The density of states is shown to exhibit the same Lifshitz tails upper bound as the integrated density of states

An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators

This version corrects the proof of Theorem 3.1.We prove that the integrated density of states (IDS) of random Schrödinger operators with Anderson-type potentials on $L^2 (\R^d)$, for $d \geq1$, is locally Hölder continuous at all energies with the same Hölder exponent $0<\alpha\leq1$ as the conditional probability measure for the single-site random variable. As a special case, we prove that if the probability distribution is absolutely continuous with respect to Lebesgue measure with a bounded density, then the IDS is Lipschitz continuous at all energies. The single-site potential $u\in L_0^\infty (\R^d)$ must be nonnegative and compactly-supported. The unperturbed Hamiltonian must be periodic and satisfy a unique continuation principle. We also prove analogous continuity results for the IDS of random Anderson-type perturbations of the Landau Hamiltonian in two-dimensions. All of these results follow from a new Wegner estimate for local random Hamiltonians with rather general probability measures

Conductivity and the current-current correlation measure

We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density at coincident energies provided the energy lies in a localization regime. The density vanishes at such energies and an upper bound on the rate of vanishing is computed. We also relate the current-current correlation measure to the localization length

Utilisation d'identifiants cryptographiques pour la sécurisation IPv6

IPv6, protocole succédant à IPv4, est en cours de déploiement dans l Internet. Il repose fortement sur le mécanisme Neighbor Discovery Protocol (NDP). Celui-ci permet non seulement à deux nœuds IPv6 de pouvoir communiquer, à l instar du mécanisme Address Resolution Protocol (ARP) en IPv4, mais il apporte aussi de nouvelles fonctionnalités, telles que l autoconfiguration d adresse IPv6. Aussi, sa sécurisation pour le bon fonctionnement de l Internet en IPv6 est critique. Son mécanisme de sécurité standardisée à l Internet Engineering Task Force (IETF) se nomme Secure Neighbor Discovery (SEND). Il s appuie à la fois sur l utilisation d identifiants cryptographiques, adresses IPv6 appelées Cryptographically Generated Addresses (CGA) et qui sont générées à partir d une paire de clés publique/privée, et de certificats électroniques X.509. L objet de cette thèse est l étude de ces identifiants cryptographiques, les adresses CGA, ainsi que le mécanisme SEND les employant, et leurs réutilisations potentielles pour la sécurisation IPv6. Dans une première partie de cette thèse, tout d abord, nous posons l état de l art. Dans une deuxième partie de cette thèse, nous nous intéressons à la fiabilité du principal mécanisme connu employant les adresses CGA, le mécanisme SEND. Dans une troisième et dernière partie de cette thèse, nous présentons des utilisations des identifiants cryptographiques pour la sécurisation IPv6IPv6, next Internet protocol after IPv4, is under deployment in the Internet. It is strongly based on the Neighbor Discovery Protocol (NDP) mechanism. First, it allows two IPv6 nodes to communicate, like the Address Resolution Protocol (ARP) mechanism in IPv4, but it brings new functions too, as IPv6 address autoconfiguration. So, the security of this mechanism is critical for an Internet based on IPv6. The security mechanism standardized by the Internet Engineering Task Force (IETF) is Secure Neighbor Discovery (SEND). It is based on the use of cryptographical identifiers, IPv6 addresses named Cryptographically Generated Addresses (CGA) and generated from a public/private keys pair, and X.509 certificates. The goal of this PhD thesis is the study of such cryptographical identifiers, CGA addresses, as well as SEND using them, and their potential re-use to secure IPv6. In a first part of this thesis, we recall the main features of the IPv6 protocol. In a second part of this thesis, we are interested in the reliability of the main known mechanism using the CGA addresses, SEND. In a third and last part of this thesis, we present different uses of cryptographical identifiers to secure IPv6EVRY-INT (912282302) / SudocSudocFranceF

Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schr\"odinger operators

We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with a constant that goes to zero as we approach the bottom of the spectrum. As an application, we show that the (differentiated) density of states exhibits the same Lifshitz tails upper bound as the integrated density of states.Comment: Revised with new titl

Effects of high doses of selenium, as sodium selenite, in septic shock: a placebo-controlled, randomized, double-blind, phase II study

INTRODUCTION: Sepsis is associated with the generation of oxygen free radicals and (lacking) decreased selenium plasma concentrations. High doses of sodium selenite might reduce inflammation by a direct pro-oxidative effect and may increase antioxidant cell capacities by selenium incorporation into selenoenzymes. We investigated the effects of a continuous administration of high doses of selenium in septic shock patients. METHODS: A prospective, multicentre, placebo-controlled, randomized, double-blind study was performed with an intention-to-treat analysis in severe septic shock patients with documented infection. Patients received, for 10 days, selenium as sodium selenite (4,000 μg on the first day, 1,000 μg/day on the nine following days) or matching placebo using continuous intravenous infusion. The primary endpoint was the time to vasopressor therapy withdrawal. The duration of mechanical ventilation, the mortality rates in the intensive care unit, at hospital discharge, and at 7, 14, 28 and 180 days and 1 year after randomization, and adverse events were recorded. RESULTS: Sixty patients were included (placebo, n = 29; selenium, n = 31). The median time to vasopressor therapy withdrawal was 7 days in both groups (95% confidence interval = 5–8 and 6–9 in the placebo and selenium groups, respectively; log-rank, P = 0.713). The median duration of mechanical ventilation was 14 days and 19 days in the placebo and selenium groups, respectively (P = 0.762). Mortality rates did not significantly differ between groups at any time point. Rates of adverse events were similar in the two groups. CONCLUSION: Continuous infusion of selenium as sodium selenite (4,000 μg on the first day, 1,000 μg/day on the nine following days) had no obvious toxicity but did not improve the clinical outcome in septic shock patients. Trial Registration = NCT00207844