Related papers: Black Holes and Marchenko-Pastur Distribution
We derive the theoretical distribution function of black hole masses by studying the formation processes of black holes. We use the results of recent 2D simulations of core-collapse to obtain the relation between remnant and progenitor…
We argue that primordial black-hole formation must be described by means of extreme-value theory. This is a consequence of the large values of the energy density required to initiate the collapse of black holes in the early Universe and the…
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in (C^d)^{otimes k}, where k and p/d^k are fixed while d grows. When k=1,…
A random matrix model of black holes is given based on analysis of Gaussian complex ensembles, based on the generalization of chRMT of QCD. Spacetime freedoms are incorporated in terms of eigenvalues of the ensemble. Classical observables…
To derive black hole thermodynamics in any quantum theory of gravity, one must introduce constraints that ensure that a black hole is actually present. For a large class of black holes, the imposition of such ``horizon constraints'' allows…
We consider the random matrix obtained by picking vectors randomly from a large collection of mutually unbiased bases of $\mathbb{C}^n$, and prove that the spectral distribution converges to the Marchenko-Pastur law. This shows that vectors…
A brief overview of the discovery that macroscopic black holes are thermodynamical systems is presented. They satisfy the laws of thermodynamics and are associated with a temperature and an entropy equal to one quarter of their horizon area…
We calculate the emergent spectrum of microscopic black holes, which emit copious amounts of thermal ``Hawking'' radiation, taking into account the proposition that (contrary to previous models) emitted quarks and gluons do not directly…
After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the…
We study the eigenvalue distributions for sums of independent rank-one $k$-fold tensor products of large $n$-dimensional vectors. Previous results in the literature assume that $k=o(n)$ and show that the eigenvalue distributions converge to…
We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments…
A central black hole can attract a dark matter cluster and generate a spike in the density profile, as demonstrated by detailed analysis of Schwarzschild and Kerr black holes in the past. Do different black holes attract dark matter…
The complex Wishart ensemble is the statistical ensemble of $M \times N$ complex random matrices with $M \geq N$ such that the real and imaginary parts of each element are given by independent standard normal variables. The Marcenko--Pastur…
We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the…
We investigate whether the Wigner semi-circle and Marcenko-Pastur distributions, often used for deep neural network theoretical analysis, match empirically observed spectral densities. We find that even allowing for outliers, the observed…
Recently, in collaboration with Susskind, we proposed a model of Schwarzschild black holes in Matrix theory. A large Schwarzschild black hole is described by a metastable bound state of a large number of D0-branes which are held together by…
The celebrated Mar\v{c}enko-Pastur law, that considers the asymptotic spectral density of random covariance matrices, has found a great number of applications in physics, biology, economics, engineering, among others. Here, using techniques…
We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. In light of improvements to the modelling, we revisit the claim that the effects of critical collapse produce a…
We calculate the energy distribution of a charged regular black hole by using the energy-momentum complexes of Einstein and M{\o}ller.
The definition of matter states on spacelike hypersurfaces of a 1+1 dimensional black hole spacetime is considered. The effect of small quantum fluctuations of the mass of the black hole due to the quantum nature of the infalling matter is…