Geoffrey Grimmett and Svante Janson Abstra t. Pick n points independently at random in R2 , according to a prescribed probability measure μ, and let ∆ 1 ≤ ∆ 2 ≤ . . . be the areas of the n 3 triangles thus formed, in non-decreasing order. If μ is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n∆ i : i ≥ 1} converges as n → ∞ to a Poisson process wi...

This paper presents a large collection of new weak-key classes for the IDEA cipher. The classes presented in this paper contain 2−2 weak keys (as compared with 2 differential weak keys presented by Daemen at CRYPTO’93 and 2 differential-linear weak-keys presented by Hawkes at EUROCRYPT’98). The novelty of our approach is in the use of boomerang distinguishers for the weak-key class membership t...

It is known that B(l) is not amenable for p = 1, 2,∞, but whether or not B(l) is amenable for p ∈ (1,∞) \ {2} is an open problem. We show that, if B(l) is amenable for p ∈ (1,∞), then so are l(B(l)) and l(K(l)). Moreover, if l(K(l)) is amenable so is l(I,K(E)) for any index set I and for any infinite-dimensional Lspace E; in particular, if l(K(l)) is amenable for p ∈ (1,∞), then so is l(K(l ⊕ l...

Institut Neel, CNRS-UJF, Nanosciences Department, 25 Av. des Martyrs, BP 166, 38042 Grenoble cedex 9, France Institut National Polytechnique de Grenoble, 46 Av. Félix Viallet, 38031 Grenoble cedex 1, France Laboratoire SPINTEC, CEA-CNRS-UJF-INPG, Bât. 1005, 17 Rue des Martyrs, 38054 Grenoble cedex 9, France Département de Mathématiques, Faculté des Sciences d'Orsay, Université Paris-Sud 11, Bât...

In this paper, we propose a procedure based on projection techniques for building exact confidence sets for covariances between errors and endogenous regressors in linear structural models. This procedure is robust to weak instruments and can be used as exogeneity test for endogenous regressors. We characterize the necessary and sufficient conditions under which these confidence sets are bounde...

Random intervals constitute one of the classes of random sets with a greater number of applications. In this paper, we regard them as the imprecise observation of a random variable, and study how to model the information about the probability distribution of this random variable. Two possible models are the probability distributions of the measurable selections and those bounded by the upper pr...

Consider a Markov process X with finite lifetime ζ. In this paper, we derive sufficient conditions which allow the conditioning of X to an infinite lifetime. This is accomplished by showing the weak convergence, as s → ∞, of the laws of (Xr : r ≤ t | ζ > s).

It is known that B(l) is not amenable for p = 1, 2,∞, but whether or not B(l) is amenable for p ∈ (1,∞) \ {2} is an open problem. We show that, if B(l) is amenable for p ∈ (1,∞), then so are l(B(l)) and l(K(l)). Moreover, if l(K(l)) is amenable so is l(I,K(E)) for any index set I and for any infinite-dimensional Lspace E; in particular, if l(K(l)) is amenable for p ∈ (1,∞), then so is l(K(l ⊕ l...

In this article, we consider three types of solutions in Orlicz spaces for the quasilinear elliptic problem − div(a(|∇u|)∇u) = 0. By applying a comparison principle, we establish the relationships between viscosity supersolutions, weak supersolutions, and superharmonic functions.