Related papers: Representation theory and random point processes
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathematics can be treated as a result of a dequantization of the…
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…
This in an introduction to the theory of non-commutative distributions of non-commuting operators or random matrices. Starting from the basic problem to find a good approach to the meaning of "non-commutative distribution" we will, in…
In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…
The aim of this work is to provide a unified framework for ordinal representations of uncertainty lying at the crosswords between possibility and probability theories. Such confidence relations between events are commonly found in monotonic…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
This paper considers the nonlinear theory of G-martingales as introduced by Peng. A martingale representation theorem for this theory is proved by using the techniques and the results established in an accompanying paper for the second…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
Sampling theory concerns the problem of reconstruction of functions from the knowledge of their values at some discrete set of points. In this paper we derive an orthogonal sampling theory and associated Lagrange interpolation formulae from…
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
This article concludes our critical analysis on the role of non-commutativity in quantum theory. After a brief introduction of the necessary notions on point processes, we re-analyse model B proposed in "On non-commutativity in quantum…
The probability representation of quantum and classical statistical mechanics is discussed. Symplectic tomography, center-of-mass tomography, and spin tomography are studied. The connection of tomographic probabilities with dynamic…
In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of \Omega is replaced with the concept of an event as a partition. The partition is any set of disjoint…