相关论文: Representation theory and random point processes

Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…

We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…

There has been an ever-increasing interest in multidisciplinary research on representing and reasoning with imperfect data. Possibilistic networks present one of the powerful frameworks of interest for representing uncertain and imprecise…

Representation theory of finite groups portrays a marvelous crossroad of group theory, algebraic combinatorics, and probability. In particular the Plancherel measure is a probability that arises naturally from representation theory, and in…

We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…

The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic…

The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…

Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional…

Current probabilistic programming languages and tools tightly couple model representations with specific inference algorithms, preventing experimentation with novel representations or mixed discrete-continuous models. We introduce a factor…

The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…

This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…

The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…

Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…

The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…

Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one…

The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…

This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…

In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…

The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…