Related papers: Bernoulli variables, classical exclusion processes…
Irreversible processes are frequently adopted to account for the entropy increase in classical thermodynamics. However, the corresponding physical origins are not always clear, e.g. in a free expansion process, a typical model in textbooks.…
We suggest a new method of calculations for a clean Fermi gas with a repulsion in any dimension. This method is based on writing equations for quasiclassical Green functions and reducing them to equations for collective spin and charge…
Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…
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…
The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two…
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The…
We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of…
We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion at rate $1$ except for a single tracer particle, which performs partially simple asymmetric exclusion with rate…
Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy,…
We have derived several relations, which allow the evaluation of the system free energy changes in the leading order in $\hbar^{2}$ along classically generated trajectories. The results are formulated in terms of purely classical…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
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…
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…
We examine the correspondence principle for an equiprobable superposition of high-energy eigenstates of the infinite square well using a fully analytical Fourier-based approach. We derive a closed-form asymptotic expression for the…
Let $f_1, f_2, ..., f_n$ be a family of independent copies of a given random variable f in a probability space $(\Omega, \mathcal{F}, \mu)$. Then, the following equivalence of norms holds whenever $1 \le q \le p < \infty$…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
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…
We establish a connection between exclusion statistics with arbitrary integer exclusion parameter $g$ and a class of random walks on planar lattices. This connection maps the generating function for the number of closed walks of given…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…