Related papers: Universal Cancellations in Uniform Random Waves
The spatial curvature of the universe is not yet known. Even though at present the Universe is very close to being essentially flat and most signatures of curvature appear to have been diluted by inflation, if the number of e-foldings…
We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry and Abelian and non-Abelian Yang-Mills…
We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant $\lambda$ are…
We investigate the spectral properties of the product of $M$ complex non-Hermitian random matrices that are obtained by removing $L$ rows and columns of larger unitary random matrices uniformly distributed on the group ${\rm U}(N+L)$. Such…
We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, a random feature model with a nonlinear activation function is asymptotically equivalent to a…
The implications of a Generalized Uncertainty Principle on the Taub cosmological model are investigated. The model is studied in the ADM reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a…
Observations of astrophysical binaries may reveal departures from pure Keplerian orbits due to environmental influences, modifications to the underlying gravitational dynamics, or signatures of new physics. In this work, we develop a…
In this paper we consider the space of those probability distributions which maximize the $q$-R\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some…
We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let $M_N$ be a deterministic $N\times N$ matrix, and let $G_N$ be a complex Ginibre matrix. We consider the matrix…
We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear…
Here we discuss some issues concerning the statistical properties of ocean surface waves. We show that, using the approach of weak turbulence theory, deviations from Gaussian statistics can be naturally included. In particular we discuss…
We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the…
We develop a fully gauge-invariant and rigorously derived framework for computing the cumulative decoherence of gravitational waves (GWs) propagating through a stochastic quantum spacetime. Working directly with the Riemann-tensor two-point…
It has long been known that particles with short-range repulsive interactions in spatial dimension d=1 form universal quantum liquids in the low density limit: all properties can be related to those of the spinless free Fermi gas. Previous…
When the semi-positive cosmological constant is dynamical, the naive Euclidean Einstein action is unbounded from below and the Hartle-Hawking wavefunction of the universe is not normalizable. With the inclusion of back-reaction (a crucial…
We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the…
The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical…
The universality observed in gravitational wave spectra of non-rotating neutron stars is analyzed here. We show that the universality in the axial oscillation mode can be reproduced with a simple stellar model, namely the centrifugal…
A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schr\"{o}dinger equation, it preserves the total energy but not the kinetic…
We present a gauge-invariant treatment of singularity resolution using loop quantum gravity techniques with respect to local SU(2) transformations. Our analysis reveals many novel features of quantum geometry which were till now hidden in…