Concentration inequalities for mean field particle models

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic perturbation analysis with a concentration analysis for triangular arrays of conditionally independent random sequences, which may be of independent interest. Under some additional stability properties of the limiting measure valued processes, uniform concentration properties, with respect to the time parameter, are also derived. The concentration inequalities presented here generalize the classical Hoeffding, Bernstein and Bennett inequalities for independent random sequences to interacting particle systems, yielding very new results for this class of models. We illustrate these results in the context of McKean-Vlasov-type diffusion models, McKean collision-type models of gases and of a class of Feynman-Kac distribution flows arising in stochastic engineering sciences and in molecular chemistry.Comment: Published in at http://dx.doi.org/10.1214/10-AAP716 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Global existence results for nonlinear Schrodinger equations with quadratic potentials

We prove that no finite time blow up can occur for nonlinear Schroedinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of the linear equation, which makes it possible to use continuity arguments and to control the nonlinear effects.Comment: Some typos fixed, Proposition 1.1 extended. Final version to appear in DCD

One more approach to the convergence of the empirical process to the Brownian bridge

A theorem of Donsker asserts that the empirical process converges in distribution to the Brownian bridge. The aim of this paper is to provide a new and simple proof of this fact

Representations of stack triangulations in the plane

Stack triangulations appear as natural objects when defining an increasing family of triangulations by successive additions of vertices. We consider two different probability distributions for such objects. We represent, or "draw" these random stack triangulations in the plane $\R^2$ and study the asymptotic properties of these drawings, viewed as random compact metric spaces. We also look at the occupation measure of the vertices, and show that for these two distributions it converges to some random limit measure.Comment: 29 pages, 13 figure

Generalizing Consistency and other Constraint Properties to Quantified Constraints

Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic properties of Constraint Satisfaction Problems (CSP), such as consistency or substitutability, are not completely understood in the quantified case. These properties are important because they are the basis of most of the reasoning methods used to solve classical (existentially quantified) constraints, and one would like to benefit from similar reasoning methods in the resolution of quantified constraints. In this paper, we show that most of the properties that are used by solvers for CSP can be generalized to quantified CSP. This requires a re-thinking of a number of basic concepts; in particular, we propose a notion of outcome that generalizes the classical notion of solution and on which all definitions are based. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalize the approach used in CSP and propose weaker, easier to check notions based on locality, which allow to detect these properties incompletely but in polynomial time

SOURCES OF JOB INFORMATION FOR MIGRANTS

Labor and Human Capital,

Loti ve eserleri

Taha Toros Arşivi, Dosya Adı: Pierre Lotiİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Living a Lie: Why Don\u27t Ask Don\u27t Tell Presents an Unworkable View of Personhood

A fundamental conflict exists between the understanding of personhood in asylum law and its conception in military law. Asylum law in the United States and the United Kingdom recognizes homosexuality as a fundamental characteristic of personhood, which cannot be concealed. Conversely, “Don’t Ask Don’t Tell,” the statutory ban on gays serving openly in the U.S. Military, demands complete suppression of any indication of homosexuality. This Comment argues that, in light of the framework for examining personhood most recently articulated by the U.K. Supreme Court, the arguments in favor of “Don’t Ask Don’t Tell” are both specious and destructive. This Comment proceeds first by examining the understanding of personhood in asylum law. It then contrasts this understanding with the demands and restrictions that “Don’t Ask Don’t Tell” imposes on homosexual military personnel. Finally, this Comment concludes by calling for a uniform application of the view of personhood found in asylum law