Related papers: Spectral fluctuations of tridiagonal random matric…
Hamilton et al. (1991) proposed a simple formula relating the nonlinear autocorrelation function of the mass distribution to the primordial spectrum of density fluctuations for gravitational clustering in an $\Omega=1$ universe. High…
We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For…
We study the eigenvector mass distribution of an $N\times N$ Wigner matrix on a set of coordinates $I$ satisfying $| I | \ge c N$ for some constant $c >0$. For eigenvectors corresponding to eigenvalues at the spectral edge, we show that the…
This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…
The structure function of a random matrix ensemble can be specified as the covariance of the linear statistics $\sum_{j=1}^N e^{i k_1 \lambda_j}$, $\sum_{j=1}^N e^{-i k_2 \lambda_j}$ for Hermitian matrices, and the same with the eigenvalues…
Not all noise in experimental measurements is unwelcome. Certain fundamental noise sources contain valuable information about the system itself -- a notable example being the inherent voltage fluctuations that exist across any resistor…
We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the…
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…
The nature of the low-frequency current fluctuations, i.e. carrier number vs. mobility, defines the strategies for noise reduction in electronic devices. While the 1/f noise in metals has been attributed to the electron mobility…
We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from inverse temperature $\beta _i$ to a final one $\beta _f$. At every time there exists a critical…
The loop equation formalism is used to compute the $1/N$ expansion of the resolvent for the Gaussian $\beta$ ensemble up to and including the term at $O(N^{-6})$. This allows the moments of the eigenvalue density to be computed up to and…
We consider dissipative dynamics of a flux qubit caused by 1/f noises, which act both on the shunting LC-contour and on the SQUID loop. These classical Gaussian noises modulate of the level splitting and of the tunnel coupling,…
We consider (AlAs)_n/(GaAs)_n superlattices with random thickness fluctuations Delta-n around the nominal period n. Using three-dimensional pseudopotential plane-wave band theory, we show that (i) any amount Delta-n/n of thickness…
There is a unique unitarily-invariant ensemble of $N\times N$ Hermitian matrices with a fixed set of real eigenvalues $a_1 > \dots > a_N$. The joint eigenvalue distribution of the $(N - 1)$ top-left principal submatrices of a random matrix…
This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the…
All members of a recently proposed new set of (non-supersymmetric) grand unified theories with at the one-loop level vanishing beta functions for the gauge, Yukawa, and scalar-boson self-interaction coupling constants are shown to involve,…
We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary…
We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much…
With the growing efforts in isolating solid-state qubits from external decoherence sources, the material-inherent sources of noise start to play crucial role. One representative example is electron traps in the device material or substrate.…
In this note, we study the Gaussian fluctuations for the Wishart matrices $d^{-1}\mathcal{X}_{n, d}\mathcal{X}^{T}_{n, d}$, where $\mathcal{X}_{n, d}$ is a $n\times d$ random matrix whose entries are jointly Gaussian and correlated with row…