In this paper we consider a class of economies with a ̄nite number of divisible commodities, linear production technologies, and indivisible goods, and a ̄nite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on ...

A fundamental theorem of Wilson states that, for every graph F , every sufficiently large F -divisible clique has an F -decomposition. Here a graph G is F -divisible if e(F ) divides e(G) and the greatest common divisor of the degrees of F divides the greatest common divisor of the degrees of G, and G has an F -decomposition if the edges of G can be covered by edge-disjoint copies of F . We ext...

Divisible e-cash systems allow a user to withdraw a wallet containingK coins and to spend k ≤ K coins in a single operation, respectively. Independent of the new work of Canard, Pointcheval, Sanders and Traoré (Proceedings of PKC ’15) we present a practical and secure divisible e-cash system in which the bandwidth of each protocol is constant while the system fulfills the standard security requ...

Let us recall some basics on infinitely divisible probability distributions or laws. We denote the set of strictly positive integers by N∗. Definition A distribution G is called infinitely divisible if for all n ∈ N∗ there exists a distribution Gn such that G equals the n-fold convolution of Gn with itself, denoted as (Gn) . In other words, the distribution of a random variable S is infinitely ...

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...