Related papers: Gaussian beta ensembles at high temperature: eigen…
Biologically driven non-equilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures…
We establish a central limit theorem for the unnormalized linear statistic of the Gaussian Unitary Ensemble under optimal conditions: the linear statistics converges if and only if the expression for the limiting variance is finite.
Let $N(L)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of ${\cal N}$ by ${\cal N}$ matrices, in the limit ${\cal…
The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic…
The problem of calculating collective density fluctuations in quantum liquids is revisited. A fully quantum mechanical self-consistent treatment based on a quantum mode-coupling theory [E. Rabani and D.R. Reichman, J. Chem. Phys.116, 6271…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop…
The Gaussian Orthogonal Ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. An important prediction is that the decay rates of the GOE eigenstates fluctuate according…
In some instances, e.g. near phase transitions, thermodynamic fluctuations become macroscopically relevant, and relative amplitudes grow far above the standard $N^{-1/2}$ scale, with $N$ the number of particles. Such large fluctuations are…
It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating…
We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained…
This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary conditions. A sharp convergence rate is obtained for isolated…
For the $\beta$-Hermite, Laguerre, and Jacobi ensembles of dimension $N$ there exist central limit theorems for the freezing case $\beta\to\infty$ such that the associated means and covariances can be expressed in terms of the associated…
We study the statistical behaviour of quantum entanglement in bipartite systems over fermionic Gaussian states as measured by von Neumann entropy. The formulas of average von Neumann entropy with and without particle number constrains have…
The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum…
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic distributions near the phase transition in…
The non-equilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301, 2004], which was announced to be a verification of the Fluctuation Relation (FR) by…
We study the thermodynamics of ultrasmall metallic grains with level spacing $\delta$ comparable or smaller than the pairing correlation energy, at finite temperatures, $T \gsim \delta$. We describe a method which allows to find quantum…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…
We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graphs $\mathcal G(N,p)$ for $p \in [N^{\varepsilon-1},N^{-\varepsilon}]$. We identify the joint limiting distributions of the…