Displaying similar documents to “A natural derivative on [0, n] and a binomial Poincaré inequality”

A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

ESAIM: Probability and Statistics

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The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function :  ×  →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.

Quasiconvexity at the boundary and concentration effects generated by gradients

Martin Kružík (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We characterize generalized Young measures, the so-called DiPerna–Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the compactification of ℝ by the sphere. We show that this characterization is closely related to the notion of quasiconvexity at the boundary introduced by Ball and Marsden [J.M. Ball and J. Marsden, 86 (1984) 251–277]. As a consequence we get new results on weak...

Means in complete manifolds: uniqueness and approximation

Marc Arnaudon, Laurent Miclo (2014)

ESAIM: Probability and Statistics

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Let be a complete Riemannian manifold,  ∈ ℕ and  ≥ 1. We prove that almost everywhere on  = ( ,, ) ∈  for Lebesgue measure in , the measure μ ( x ) = N ∑ k = 1 N x k μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if  = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...

Trivial Cases for the Kantorovitch Problem

Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)

RAIRO - Operations Research

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Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal....

Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément Mouhot, Lorenzo Pareschi, Thomas Rey (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically ( ) where is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, 339 (2004) 71–76, C. Mouhot and L. Pareschi, 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of discrete-velocity schemes which...

Survival probabilities of autoregressive processes

Christoph Baumgarten (2014)

ESAIM: Probability and Statistics

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Given an autoregressive process of order (  =   + ··· +   +  where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...

An Extended Opportunity-Based Age Replacement Policy

Bermawi P. Iskandar, Hiroaki Sandoh (2010)

RAIRO - Operations Research

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The present study proposes an extended opportunity-based age replacement policy where opportunities occur according to a Poisson process. When the age, of the system satisfies for a prespecified value , a corrective replacement is conducted if the objective system fails. In case satisfies for another prespecified value , we take an opportunity to preventively replace the system by a new one with probability , and do not take the opportunity with probability . At the moment reaches...

KPZ formula for log-infinitely divisible multifractal random measures

Rémi Rhodes, Vincent Vargas (2011)

ESAIM: Probability and Statistics

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We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. 236 (2003) 449–475]. If is a non degenerate multifractal measure with associated metric () = ([]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dim of a measurable set and the Hausdorff dimension dim with respect to of the same set: ζ(dim ()) = dim(). Our results...

On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Lorenzo Brasco (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We generalize to the -Laplacian a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of of a set in terms of its -torsional rigidity. The result is valid in every space dimension, for every 1    ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants....

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( =   < 1), or is much greater than ...

Upper large deviations for maximal flows through a tilted cylinder

Marie Theret (2014)

ESAIM: Probability and Statistics

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We consider the standard first passage percolation model in ℤ for  ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to and whose height is () for a certain height function . We denote this maximal flow by (respectively ). We emphasize the fact that the cylinder may be tilted. We look at the probability that...