Related papers: Hole Probability for Entire Functions represented …
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…
General relativity predicts the existence of black holes, compact objects whose spacetimes depend on only their mass, spin, and charge in vacuum (the "no hair" theorem). As various observations probe deeper into the strong fields of black…
In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of…
We study the behavior of the tail probabilities $P(V^2<r)$ as $r\to 0$, where $V^2$ is defined by the following double sum $$ V^2 =\pi^{-4}\,\sum\limits_{i,j\ge 1} \Big((i+b)\,(j + \delta)\Big)^{-2}\,\xi_{ij}^2,$$ where $ \{\xi_{ij}\} $ are…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
We offer new Tauberian theorems for a generalized partition function as our main result. Our analysis provides insight into asymptotic behavior of power series with arithmetic functions as coefficients.
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
The growing interest of different entropy functions proposed so far (like the Bekenstein-Hawking, Tsallis, R\'{e}nyi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies) towards black hole thermodynamics as well as towards…
In this paper we study the issue of the role of nonlocality as a possible ingredient to solve long standing problems in the physics of black holes. To achieve this goal we analytically derive new black hole metrics improved by corrections…
We study L^p properties of Gaussian random series with particular attention to the case of radial functions.
We investigate the probability that a random polynomial with independent, mean-zero and finite variance coefficients has no real zeros. Specifically, we consider a random polynomial of degree $2n$ with coefficients given by an i.i.d.…
We present a new initial data formulation to solve the full set of Einstein equations for spacetimes that contain a black hole under general conditions. The method can be used to construct complete initial data for spacetimes (the full…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on…
For a scalar Gaussian process $B$ on $\mathbb{R}_{+}$ with a prescribed general variance function $\gamma^{2}\left(r\right) =\mathrm{Var}\left(B\left(r\right) \right) $ and a canonical metric $\mathrm{E}[\left(B\left(t\right)…
We describe an expansion of Legendre polynomials, analogous to the Taylor expansion, to approximate arbitrary functions. We show that the polynomial coefficients in Legendre expansion, therefore the whole series, converge to zero much more…
Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…
Tidal Love numbers of black holes, zero in classical general relativity for Kerr black holes in vacuum, become non-vanishing in the presence of exotic matter or in alternative theories of gravity, making them a powerful probe of fundamental…
Configurations of rotating black holes in the cubic Galileon theory are computed by means of spectral methods. The equations are written in the 3+1 formalism and the coordinates are based on the maximal slicing condition and the spatial…
We trace with analytical methods and in a model parameter independent manner the independent bits of Fisher information of each of the moments of the lognormal distribution, as a now standard prescription for the distribution of the…