相关论文: On Generalized Statistics and Interactions

Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…

Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…

An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…

An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…

Several different types of statistical interaction are defined and distinguished, primarily on the basis of the nature of the factors defining the interaction. Illustrative examples, mostly epidemiological, are given. The emphasis is…

When animal groups move coherently in the form of a flock, their trajectories are not all parallel, the individuals exchange their position in the group. In this Letter we introduce a measure of this mixing dynamics, which we quantify as…

An oscillator algebra and the associated Fock space with reflecting boundary and generalized statistics are constructed and is generalized to the multicomponent case. The oscillator algebra depends manifestly on the reflection factor and…

The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…

Closed-form expressions for the distributions of the order statistics on the spacings between order statistics for the uniform distribution are obtained. This generalizes a result by Fisher concerning tests of significance in the harmonic…

The model of generalized quons is described in a purely algebraic way. Commutation relations and corresponding consistency conditions for our generalized quons system are studied in terms of quantum Weyl algebras. Fock space representation…

In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by…

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can…

We present a discussion of generalized statistics based on Renyi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of…

It has been shown recently that Bose Gase with weak pair (enough well) interaction is non ergodic system. But Bose Gase with weak pair interaction is so general system that it is evident that the majority of statistical mechanics systems…

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and nonliving matter. Group interactions are a particularly important and widespread class,…

The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…