Related papers: A multivariate generalization of Costa's entropy p…
It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the…
We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and…
In this paper we consider the problem of a measure that allows us to describe the spatial and temporal dependence structure of multivariate time series with innovations having infinite variance. By using recent results obtained in the…
We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…
The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential, and time dependent force, we study the subdiffusion…
Almost all modern communication systems rely on electromagnetic fields as a means of information transmission, and finding the capacities of these systems is a problem of significant practical importance. The Additive White Gaussian Noise…
We prove the longstanding conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant…
Recent development of the resonance scattering theory with a transient from the regular to chaotic internal dynamics inspires renewed interest to the problem of the elastic enhancement phenomenon. We reexamine the question what the…
Uncertainty principle plays a crucial role in quantum mechanics, because it captures the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Information entropy can perfectly describe…
The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial…
This paper considers the problem of appearance indication of useful acoustic signal in the signal/noise mixture. Various information characteristics (information entropy, Jensen-Shannon divergence, spectral information divergence and…
From K\"ummerer's investigations on stationary Markov processes has emerged an operator algebraic definition of white noises which captures many examples from classical as well as from non-commutative probability. Within non-commutative…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…
We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is…
Noise is a vital factor in determining the accuracy of processing the information of the quantum channel. One must consider classical noise effects associated with quantum noise sources for more realistic modelling of quantum channels. A…
We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure.…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
We show that $h_\infty(X+Y)\leq h_\infty(Z+W)$, where $X, Y$ are independent log-concave random variables, and $Z, W$ are exponential random variables having the same respective $\infty$-R\'enyi entropies. Analogs for integer-valued…