Related papers: A universality result for subcritical Complex Gaus…
Recently, there has been a growing interest for mixed-categorical meta-models based on Gaussian process (GP) surrogates. In this setting, several existing approaches use different strategies either by using continuous kernels (e.g.,…
We prove the quantitative propagation of chaos for stochastic particle systems with interaction in both the drift and the diffusion coefficients, provided the drift kernel is bounded and free of Lipschitz or smoothness assumptions. Our…
In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…
Chaos in Robertson-Walker cosmological models where gravity is coupled to one or more scalar fields has been studied by a few authors, mostly using numerical simulations. In this paper we begin a systematic study of the analytical aspect.…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…
We introduce a novel relaxation of combinatorial discrepancy called Gaussian discrepancy, whereby binary signings are replaced with correlated standard Gaussian random variables. This relaxation effectively reformulates an optimization…
Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
We discuss the classical and quantum chaos of closed strings on a recently constructed charged confining holographic background. The confining background corresponds to the charged soliton, which is a solution of minimal $d=5$ gauged…
It is shown that appearance of inertial range of scales, adjacent to distributed chaos range, results in adiabatic invariance of an energy correlation integral for isotropic homogeneous turbulence and for buoyancy driven turbulence (with…
This paper presents an elementary proof of quantitative uniform-in-time propagation of chaos for the Cucker--Smale model under sufficiently strong interaction. The idea is to combine existing finite-time propagation of chaos estimates with…
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical…
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…
We develop a systematic method of the perturbative expansion around the Gaussian effective action based on the background field method. We show, by applying the method to the quantum mechanical anharmonic oscillator problem, that even the…
This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…
We study how the Gaussian multiplicative chaos (GMC) measures $\mu^\gamma$ corresponding to the 2D Gaussian free field change when $\gamma$ approaches the critical parameter $2$. In particular, we show that as $\gamma\to 2^{-}$,…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
The difficulties of perturbation theory associated with unstable fundamental fields (such as the lack of exact gauge invariance in each order) are cured if one constructs perturbative expansion directly for probabilities interpreted as…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…