Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by Σ, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new context. For instance, an operator space is BΣ-convex if and only if it has Σ-subtype. The class of uniformly non-L(Σ) operator spaces, which is also the class of BΣ-conve...

In this work, we are interested in the spectrum of the diffusively excited granular gases equation, in a space inhomogeneous setting, linearized around an homogeneous equilibrium. We perform a study which generalizes to a non-hilbertian setting and to the inelastic case the seminal work of Ellis and Pinsky [8] about the spectrum of the linearized Boltzmann operator. We first give a precise loca...

We discuss some problems and permutation statistics involving two different types of random permutations. Under the usual model of random permutations, we prove that the shifted coverage of the elements of {1, 2, . . . , k} of a random permutation over {1, 2, . . . , n}; that is, the size of the union of the cycles containing these elements, excluding these elements themselves, follows a negati...