Related papers: Wick polynomials and time-evolution of cumulants

Given an ordered set partition, when one insert a number of bars in-between the blocks of the ordered set partition the result is a barred preferential arrangement. In this study, using the notion of barred preferential arrangements we…

We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such…

We compute the expansion of the cohomology class of the permutahedral variety in the basis of Schubert classes. The resulting structure constants $a_w$ are expressed as a sum of \emph{normalized} mixed Eulerian numbers indexed naturally by…

We prove decoupling inequalities for random polynomials in independent random variables with coefficients in vector space. We use various means of comparison, including rearrangement invariant norms (e.g., Orlicz and Lorentz norms), tail…

In this paper, it is proved that, in a dual context, asymptotic expansions of ordinary linear time-differential equations which possess limiting equations to their limiting equations might be obtained by first discretizing them and then…

The paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete, and the binary aggregation alone governs the time evolution of the systems. By considering the growth…

Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a "broken exponential martingale" expansion that generalizes and unifies the exponentiation result of…

Given two polynomials $p(x), q(x)$ of degree $d$, we give a combinatorial formula for the finite free cumulants of $p(x)\boxtimes_d q(x)$. We show that this formula admits a topological expansion in terms of non-crossing multi-annular…

We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d…

A formula expressing free cumulants in terms of the Jacobi parameters of the corresponding orthogonal polynomials is derived. It combines Flajolet's theory of continued fractions and Lagrange inversion. For the converse we discuss…

Factorial moments and cumulants are usually defined with respect to the unconditioned Poisson process. Conditioning a sample by selecting events of a given overall multiplicity $N$ necessarily introduces correlations. By means of Edgeworth…

In this work, we investigate the approach via flipclasses to the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials of all Coxeter groups. We prove the combinatorial invariance of Kazhdan--Lusztig…

We introduce a new approach for generating combinatorial identities and formulas by the application of Kronecker substitution to polynomial expansions within quotient rings. Our main result enables the derivation of elementary arithmetic…

We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have…

A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…

We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit…

We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show…

The quantum statistics of damped optical solitons is studied using cumulant-expansion techniques. The effect of absorption is described in terms of ordinary Markovian relaxation theory, by coupling the optical field to a continuum of…