Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces.
Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene II.
Maße für gerichtete Geraden und nicht-symmetrische Pseudometriken in der Ebene.
Matchings and the variance of Lipschitz functions
We are interested in the rate function of the moderate deviation principle for the two-sample matching problem. This is related to the determination of 1-Lipschitz functions with maximal variance. We give an exact solution for random variables which have normal law, or are uniformly distributed on the Euclidean ball.
Means in complete manifolds: uniqueness and approximation
Let M be a complete Riemannian manifold, M ∈ ℕ and p ≥ 1. We prove that almost everywhere on x = (x1,...,xN) ∈ MN for Lebesgue measure in MN, the measure μ ( x ) = 1 N ∑ k = 1 N δ x k has a uniquep–mean ep(x). As a consequence, if X = (X1,...,XN) is a MN-valued random variable with absolutely continuous law, then almost surely μ(X(ω)) has a unique p–mean. In particular if (Xn)n ≥ 1 is an independent sample of an absolutely continuous law in M, then the process ep,n(ω) = ep(X1(ω),...,Xn(ω)) is...
Measurability of classes of Lipschitz manifolds with respect to Borel -algebra of Vietoris topology
Mesures singulières associées à des découpages aléatoires d'un hypercube
Metric Diophantine approximation on the middle-third Cantor set
Let be a real number and let denote the set of real numbers approximable at order at least by rational numbers. More than eighty years ago, Jarník and, independently, Besicovitch established that the Hausdorff dimension of is equal to . We investigate the size of the intersection of with Ahlfors regular compact subsets of the interval . In particular, we propose a conjecture for the exact value of the dimension of intersected with the middle-third Cantor set and give several results...
Moderate deviation principles for sums of i.i.d. random compact sets
We prove a moderate deviation principle for Minkowski sums of i.i.d. random compact sets in a Banach space.
Moderate deviations for some point measures in geometric probability
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy moderate deviation principles. This leads to moderate deviation principles and laws of the iterated logarithm for random packing models as well as for statistics associated with germ-grain models and k nearest neighbor graphs.