Related papers: Scott Continuity in Generalized Probabilistic Theo…

The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…

We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda\to\infty$ limit of general relativity. This allows an…

We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…

Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems, both as a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy…

By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…

The aim of this paper is to suggest a new interpretation of quantum indeterminacy using the notion of polar duality from convex geometry. Our approach does not involve the usual variances and covariances, whose use to describe quantum…

This paper establishes a purely syntactic representation for the category of algebraic L-domains with Scott-continuous functions as morphisms. The central tool used here is the notion of logical states, which builds a bridge between…

A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference and velocity gradient are derived. No closure assumptions…

Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…

Matthew de Brecht raised the question of whether countable frames are continuous lattices. We prove that the continuity of a countable frame implies the quasicontinuity of its corresponding spectrum in the dual specialization order. We…

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…

In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, infinitesimal random variables. The theory is shown to parallel the classical theory of independent random…

Let $x_1,x_2,...,x_n$ be the zeroes of a polynomial P(x) of degree n and $y_1,y_2,...,y_m$ be the zeroes of another polynomial Q(y) of degree m. Our object of study is the permanent $\per(1/(x_i-y_j))_{1\le i\le n, 1\le j\le m}$, here named…

Bosbach states represent a way of probabilisticly evaluating the formulas from various (commutative or non-commutative) many-valued logics. They are defined on the algebras corresponding to these logics with values in $[0,1]$. Starting from…

This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…

The Darmois-Skitovich theorem is a simple characterization of the normal distribution in terms of the independence of linear forms. We present here a non-commutative version of this theorem in the context of Gaussian bosonic states and show…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…

``Constants of Nature'' and cosmological parameters may in fact be variables related to some slowly-varying fields. In models of eternal inflation, such fields will take different values in different parts of the universe. Here I show how…

We study a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbations via an additive Gaussian noise. We show that for a broad…

Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains…