相关论文: Non-Universality of Nodal Length Distribution for …

In this paper, we have considered a toy model of an anisotropic universe and studied the propagation of gravitational waves in such a universe. The consideration of this toy model simplifies the analysis and helps us to illustrate the…

In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical…

We study random waves on smooth, compact, Riemannian manifolds under the spherical ensemble. Our first main result shows that there is a positive universal limit for the critical radius of a specific deterministic embedding, defined via the…

In this work, we establish conditions ensuring convergence in distribution of a sequence admitting a Wiener-It\^o chaos representation to a nondegenerate Gaussian measure on a separable Hilbert space. Our first main result shows that,…

Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…

Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and…

We examine isotropic and anisotropic random walks which begin on the surface of linear ($N$), square ($N \times N$), or cubic ($N \times N \times N$) lattices and end upon encountering the surface again. The mean length of walks is equal to…

Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…

We study real left-invariant spin Gaussian fields on $SO(3)$, a special class of non-isotropic random fields used to model the polarization of the Cosmic Microwave Background. Leveraging recent results from "New chaos decomposition of…

Nonlinear wave propagation in large extra spatial dimensions (on and above $d=2$) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant…

A two-dimensional system of non-locally coupled complex Ginzburg-Landau oscillators is investigated numerically for the first time. As already known for the one-dimensional case, the system exhibits anomalous spatio-temporal chaos…

The intrinsic dynamical complexity of classically chaotic systems enforces a universal description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear…

An alternative formulation of the no-boundary initial state of the universe in the Euclidean quantum theory of gravity is proposed. Unlike the no-boundary Hartle-Hawking wave function, in which time appears together with macroscopic…

The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…

Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…

We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the…

We consider a stochastic wave equation in spatial dimension three, driven by a Gaussian noise, white in time and with a stationary spatial covariance. The free terms are nonlinear with Lipschitz continuous coefficients. Under suitable…

Distribution amplitudes are functions of non-perturbative matrix elements describing the hadronization of quarks and gluons. Thanks to factorization theorems, they can be used to compute the scattering amplitude of high-energy processes.…

We analytically investigate the nonautonomous discrete rogue wave solutions and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, which possess complicated wave propagations in time and are…

For a centered $d$-dimensional Gaussian random vector $\xi =(\xi_1,\ldots,\xi_d)$ and a homogeneous function $h:R^d\to R$ we derive asymptotic expansions for the tail of the Gaussian chaos $h(\xi)$ given the function $h$ is sufficiently…