For various classes of Lipschitz functions we provide dimension free concentration inequalities for infinitely divisible random vectors with independent components and finite exponential moments. The purpose of this note is to further visit the concentration phenomenon for infinitely divisible vectors with independent components in an attempt to obtain dimension free concentration. Let X ∼ ID(γ...

The so-called Bercovici-Pata bijection maps the set of classical infinitely divisible laws to the set of free infinitely divisible laws. The purpose of this work is to study the free infinitely divisible laws corresponding to the classical Generalized Gamma Convolutions (GGC). Characterizations of their free cumulant transforms are derived as well as free integral representations with respect t...

The non-Markovianity of the stochastic process called quantum semi-Markov (QSM) is studied using a recently proposed quantification memory based on deviation from semigroup evolution, that provides unified description divisible and indivisible channels. This shown to bring out property QSM processes exhibit effects even in CP-divisible regime, agreement with an earlier result. An operational me...

The use of divisible load scheduling theory is proposed to model and design grid systems such as those arising in large physics experiments. Current divisible load theory is summarized. A typical application, the STAR experiment at RHIC is discussed. This includes a sample calculation based on existing infrastructure numbers.

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels’ transmission rates.

We introduce two new infinite families of APN functions, one on fields of order 22k for k not divisible by 2, and the other on fields of order 23k for k not divisible by 3. The polynomials in the first family have between three and k+ 2 terms, the second family’s polynomials have three terms. © 2007 Elsevier Inc. All rights reserved.

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space. AMS Classification: 05B05, 05B30, 20B25, 51N10

H. Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, showed how to use amicable sets of matrices to construct orthogonal designs in orders divisible by eight. We show how amicable orthogonal designs can be used to make amicable sets and so obtain infinite families of orthogonal designs in six variables in orders divisible by eight.

Abstract. Two methods to approximate infinitely divisible random fields are presented. The methods are based on approximating the kernel function in the spectral representation of such fields, leading to numerical integration of the respective integrals. Error bounds for the approximation error are derived and the approximations are used to simulate certain classes of infinitely divisible rando...

Subspace codes, i.e., subset of a finite-field Grassmannian, are applied in random linear network coding. Here we give improved upper bounds based on the Johnson bound and a connection to divisible codes, which is presented in a purely geometrical way. This complements a recent approach for upper bounds on the maximum size of partial spreads based on projective qr-divisible codes.