Related papers: The Universal Generating Function of Analytical Po…

Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the…

Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…

In this article we construct a generalized Gaussian process coming from Coxeter groups of type B. It is given by creation and annihilation operators on an $(\alpha,q)$-Fock space, which satisfy the commutation relation $$…

The standard Poisson structure on the rectangular matrix variety M_{m,n}(C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus T of GL_{m+n}(C). These orbits, finite in number, are shown to be smooth…

The problem of characterizing all new-time transformations preserving the Poisson structure of a finitedimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously…

By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is…

We investigate in this short article the fundamental function for the so-called Grand Lebesgue Spaces (GLS) and show in particular a one-to-one and mutually continuous accordance between its fundamental and generating function.

A formula for the generating function of the Weil-Petersson volumes of moduli spaces of pointed curves that is identical to the genus expansion of the free energy in two dimensional gravity is obtained. The contribution of arbitrary genus…

We recall the fat-graph description of Riemann surfaces $\Sigma_{g,s,n}$ and the corresponding Teichm\"uller spaces $\mathfrak T_{g,s,n}$ with $s>0$ holes and $n>0$ bordered cusps in the hyperbolic geometry setting. If $n>0$, we have a…

A q-generalization of the product densities in stochastic point processes is developed. The properties of these functions are studied and a q-generalization of the usual $C^r_s$ coefficients is obtained. This for fixed q-number of particles…

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY…

This work is devoted to the establishment of a Poisson structure for a format of equations known as Generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been…

We construct symplectic groupoids integrating log-canonical Poisson structures on cluster varieties of type $\mathcal{A}$ and $\mathcal{X}$ over both the real and complex numbers. Extensions of these groupoids to the completions of the…

In this paper we prove superintegrability of Hamiltonian systems generated by functions on $K\backslash G/K$, restriced to a symplectic leaf of the Poisson variety $G/K$, where $G$ is a simple Lie group with the standard Poisson Lie…

The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in…

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold.…

Coadjoint orbits and multiplicity free spaces of compact Lie groups are important examples of symplectic manifolds with Hamiltonian groups actions. Constructing action-angle variables on these spaces is a challenging task. A fundamental…

This paper is a fusion of a survey and a research article. We focus on certain rigidity phenomena in function spaces associated to a symplectic manifold. Our starting point is a lower bound obtained in an earlier paper with Zapolsky for the…

This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…

We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…