Related papers: Analysis on Poisson and Gamma spaces
This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the…
In this thesis, we study deformations of compact holomorphic Poisson manifolds and algebraic Poisson schemes in the framework of Kodaira-Spencer's analytic deformation theory and Grothendieck's algebraic deformation theory.
New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are provided by conditions on these tensors, which may be understood as cocycle…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
We extend the inner product from bosonic Fock space to a pairing between suitable antifunctionals on the symmetric algebra. Our account is illustrated by the (Gaussian) half-form pairing between positive polarizations in the form needed for…
We study the effect of a non-Gaussian noise on interstate switching activated primarily by Gaussian noise. Even weak non-Gaussian noise can strongly change the switching rate. The effect is determined by all moments of the noise…
A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…
We are developing a new method for the analysis of queuing systems with heterogeneous in time and space compound (marked) Poisson input flow. The state space of the input flow is embedded in a higher-dimensional space with a homogeneous…
In this paper we define a canonical Poisson structure on a normal generalized contact metric space and use this structure to define a generalized Sasakian structure. We show also that this canonical Poisson structure enables us to…
Here we present an overview of countably-normed spaces. We discuss the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and discuss the sigma-fields generated by these topologies. In particular,…
In this article, we discuss some recent developments of the Zariski Cancellation Problem in the setting of noncommutative algebras and Poisson algebras.
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
We have analyzed the phenomenon of stochastic resonance in a system driven by non Gaussian noises. We have considered both white and colored noises. In the latter case we have obtained a consistent Markovian approximation that enables us to…
We introduce a noncommutative Poisson random measure on a von Neumann algebra. This is a noncommutative generalization of the classical Poisson random measure. We call this construction Poissonization. Poissonization is a functor from the…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
We study Jacobi pairs in details and obtained some properties. We also study the natural Poisson algebra structure $(\PP,[...,...],...)$ on the space $\PP:=\C[y]((x^{-\frac1N}))$ for some sufficient large $N$, and introduce some…
A compact semisimple Lie algebra $\mathfrak{g}$ induces a Poisson structure $\pi$ on the unit sphere $S$ in $\mathfrak{g}^*$. We compute the moduli space of Poisson structures on $S$ around $\pi$. This is the first explicit computation of a…