相关论文: Free Meixner states
Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for fermions. Some state vectors describe infinitely…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
We theoretically introduce a new kind of non-Gaussian state-----Laguerre polynomial excited coherent states by using the multiphoton catalysis which actually can be considered as a block comprising photon number operator. It is found that…
Two-mode charge (pair) coherent states has been introduced previously by using $<\eta|$ representation. In the present paper we reobtain these states by a rather different method. Then, using the nonlinear coherent states approach and based…
We obtain a family of polynomials defined by vanishing conditions and associated to tangles. We study more specifically the case where they are related to a O(n) loop model. We conjecture that their specializations at $z_i=1$ are {\it…
It is well known that a nontrivial commutator in a free group is never a proper power. We prove a theorem that generalizes this fact and has several worthwhile corollaries. For example, an equation $[ x_1, y_1] \ldots [ x_k, y_k] = z^n$,…
We consider noncommutative rational functions as well as matrices in polynomials in noncommuting variables in two settings: in an algebraic context the variables are formal variables, and their rational functions generate the "free field";…
We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-$D$ Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the…
We study the decomposition of free random variables in terms of their orthogonal replicas from a new perspective. First, we show that the mixed moments of orthogonal replicas with respect to the normalized linear functional $\Phi$ are…
The main purpose of this article is to provide new results on algebraic independence of values of Mahler functions and their generalizations. Simultaneously, we establish new measures of algebraic independence for these values. Among the…
In this paper, we give a description of polynomial functors from (finitely generated free) groups to abelian groups in terms of non-linear Mackey functors generalizing those given in a paper of Baues-Dreckmann-Franjou-Pirashvili published…
Free cumulants were introduced by Speicher as a proper analog of classical cumulants in Voiculescu's theory of free probability. The relation between free moments and free cumulants is usually described in terms of Moebius calculus over the…
We study the vacuum distribution, under an appropriate scaling, of a family of partial sums of nonsymmetric position operators on weakly monotone and monotone Fock spaces, respectively. We preliminary treat the case of weakly monotone Fock…
We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then…
We present a perturbative construction of two kinds of eigenfunctions of the commuting family of difference operators defining the elliptic Ruijsenaars system. The first kind corresponds to elliptic deformations of the Macdonald…
Using the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal, gamma, and Poisson exponential families. Replacing the…
A real Milnor manifold is the non-singular hypersurface of degree $(1,1)$ in the product of two real projective spaces. These manifolds were introduced by Milnor to give generators for the unoriented cobordism algebra, and they admit free…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We consider the Schr\"odinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold $0$.…
We construct the coherent states of general order, $m$ for the ladder operators, $c(m)$ and $c^\dagger(m)$, which act on rational deformations of the harmonic oscillator. The position wavefunctions of the eigenvectors involve type III…