Related papers: Generalized Riffle Shuffles and Quasisymmetric Fun…

In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, \emph{Derivation and double shuffle relations for multiple zeta…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…

In this paper we classify when (row-strict) dual immaculate functions and (row-strict) extended Schur functions, as well as their skew generalizations, are symmetric. We also classify when their natural variants, termed advanced functions,…

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…

We consider groupoids on $\{1,2,..,d\}^\mathbb{N}$, cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eigenprobabilities for the dual of the Ruelle operator. We…

We develop the general theory of Jack-Laurent symmetric functions, which are certain generalisations of the Jack symmetric functions, depending on an additional parameter p_0.

A family of random probabilities is defined and studied. This family contains the Dirichlet process as a special case, corresponding to an inner point in the appropriate parameter space. The extension makes it possible to have random means…

We consider the distribution of the binomial probability mass function (pmf) among arithmetic progressions and obtain an average-type theorem. As applications, we consider the possible visits to a kind of sieved sets of integers or lattice…

Eulerian quasisymmetric functions were introduced by Shareshian and Wachs in order to obtain a q-analog of Euler's exponential generating function formula for the Eulerian numbers. They are defined via the symmetric group, and applying the…

We find in measurements of microwave transmission through quasi-1D dielectric samples for both diffusive and localized waves that the field normalized by the square root of the spatially averaged flux in a given sample configuration is a…

We determine the probability distribution for the field inside a random uniform distribution of electric or magnetic dipoles. For parallel dipoles, simulations and an analytical derivation show that although the average contribution from…

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…

We explore some probabilistic applications arising in connections with $K$-theoretic symmetric functions. For instance, we determine certain corner distributions of random lozenge tilings and plane partitions. We also introduce some…

This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider are represented as smoothed averages of spherical Gaussian…

We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the…

We study the factorization of quasi generalized quark distributions with twist-2 generalized parton distributions. We use an approach which is different than that used in literature. Using the approach we derive the factorization relations…

Level and wavefunction statistics have been studied for two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2) Phi_0 and (1/2)…

We introduce a quasisymmetric class function associated with a group acting on a double poset or on a directed graph. The latter is a generalization of the chromatic quasisymmetric function of a digraph introduced by Ellzey, while the…