Related papers: The Fourth-Order Correlation Function of a Randoml…
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…
We compute the fourth order action in perturbation theory for scalar and second order tensor perturbations for a minimally coupled single field inflationary model, where the inflaton's lagrangian is a general function of the field's value…
We consider a scalar field governed by an advection-diffusion equation (or a more general evolution equation) with rapidly fluctuating, Gaussian distributed random coefficients. In the white noise limit, we derive the closed evolution…
The stochastic approach to calculating scalar correlation functions in de Sitter spacetime is extended beyond the overdamped "slow roll" approximation. We show that with the correct noise term, it reproduces the exact asymptotic…
We investigate horizontal dispersion of a passive scalar in a porous stratum with Rayleigh-Darcy convection initiated by a geothermal gradient. While increasing Rayleigh number ($Ra$) keeps enhancing convection, the horizontal dispersion…
Analytical templates for the 4-Point Correlation Function (4PCF) covariance matrix have been developed in the past assuming a Gaussian Random Field (GRF). In this work, we present the second part of the beyond GRF calculation of the 4PCF…
As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the…
Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The…
The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
We consider the slowly rotating relativistic stars with a uniform angular velocity in the scalar-tensor gravity, and examine the rotational effect around such compact objects. For this purpose, we derive a 2nd order differential equation…
We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations $(h)$ of the background metric, in the flat spacetime limit. For this purpose we discuss the…
Spatial data display correlation between observations collected at neighboring locations. Generally, machine and deep learning methods either do not account for this correlation or do so indirectly through correlated features and thereby…
We consider an infrared truncated massless minimally coupled scalar field with a quartic self-interaction in the locally de Sitter background of an inflating universe. We compute the two-point correlation function of the scalar at one and…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality $d$ of space and the degree of compressibility of the smooth advecting velocity field, the cascade of…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
A compressible generalization of the Kraichnan model (Phys. Rev. Lett. 72, 1016 (1994)) of passive scalar advection is considered. The dynamical role of compressibility on the intermittency of the scalar statistics is investigated for the…