Equidistributed random variables in Lp, q

On the LP-convergence for multidimensional arrays of random variables

Let Z+, where d is an integer, denote the positive integer d-dimensional lattice points. The notation m≺ n, where m= (m1,m2, . . . ,md) and n= (n1,n2, . . . ,nd) ∈ Z+, means that mi ≤ ni, 1 ≤ i≤ d, |n| is used for ∏d i=1ni. Gut [2] proved that if {X ,Xn, n∈ Z+} is a d-dimensional array of i.i.d. random variables with E|X|p <∞ (0 < p < 2) and EX = 0 if 1 ≤ p < 2, then ∑ j≺nXj |n|1/p −→ 0 in L p ...

THE NORM OF SUMS OF INDEPENDENT NONCOMMUTATIVE RANDOM VARIABLES IN Lp(l1)

We investigate the norm of sums of independent vector-valued random variables in noncommutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class S q in Sp(lmq ) with optimal order m ∼ n. Using these embeddings we show the surprising fact that the sharp type (cotype) index in the sense of operator spaces for Lp[0, 1] is min(p, p) (max(p, p)). Simi...

COMBINATORICS OF GEOMETRICALLY DISTRIBUTED RANDOM VARIABLES: NEW q-TANGENT AND q-SECANT NUMBERS

Up-down permutations are counted by tangent (respectively, secant) numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all coincide with the classical version. In this way, we get some new q-tangent and q-secant functions. Some of them also have nice continued fraction ex...

The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball

Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for generalized Orlicz balls. This allows us to give a strong concentration property, along with a few moment comparison inequalities. Also, the theory of negatively as...

Central and Local Limit Theories in Markov Dependent Random Variables