Related papers: Quantum De Moivre-Laplace theorem for noninteracti…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
The problem to express a natural number N as a product of natural numbers without regard to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional potential with logarithmic energy eigenvalues. This…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable then the measurement outcome of that observable is…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We quantify the intrinsic noise content of an observable in a general probabilistic theory and derive a noise content inequality for incompatible observables. We apply the derived inequality to standard quantum theory, the quantum theory of…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
The s=3/2 Ising spin chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field is shown to be equivalent to a system of 17 species of particles with internal structure. The same set of particles (with…
A simple relativistic quantum hidden-variable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum…
In this paper, we develop asymptotic theory for the mixing detection methodology proposed by M. Magdziarz and A. Weron [Physical Review E, 84:051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes including…
With a graph $G=(V,E)$ we associate a collection of non-negative real weights $\cup_{v\in V}{\lambda_{i,v}:1\leq i \leq m} \cup \cup_{uv \in E} {\lambda_{ij,uv}:1\leq i \leq j \leq m}$. We consider the probability distribution on…
Probabilities of photon counts at the output of a multiport optical device are generalised for optical sources of arbitrary quantum states in partially distinguishable optical modes. For the single-mode photon sources, the generating…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
In this paper, we discuss P(n), the number of ways in which a given integer n may be written as a sum of primes. In particular, an asymptotic form P_as(n) valid for n towards infinity is obtained analytically using standard techniques of…
We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type…
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…