相关论文: On Fluctuations of Matrix Entries of Regular Funct…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
This paper develops an inferential framework for matrix completion when missing is not at random and without the requirement of strong signals. Our development is based on the observation that if the number of missing entries is small…
Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…
We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real…
We consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J.…
It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…
It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation…
We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix $H$ converge to the Tracy-Widom laws at a rate nearly $O(N^{-1/3})$, as the matrix dimension $N$ tends to infinity. We allow the variances of the…
We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes, or between integrable and non-integrable systems. We derive analytical formulas for the spacing…
We study the non-equilibrium stationary fluctuations of a symmetric zero-range process on the discrete interval $\{1, \ldots, N-1\}$ coupled to reservoirs at sites $1$ and $N-1$, which inject and remove particles at rates proportional to…
The equivalence of regularity of a Q-matrix with its bounded perturbations is proved and a integration by parts formula is established for the associated Feller minimal transition functions.
In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet.
We consider the ``visible'' Wigner matrix, a Wigner matrix whose $(i, j)$-th entry is coerced to zero if $i, j$ are co-prime. Using a recent result from elementary number theory on co-primality patterns in integers, we show that the…
The second part of the article is devoted to field transfers by diffraction that are represented by fractional Fourier transformations whose orders are complex numbers. The corresponding effects on the Wigner distributions associated with…
In this short note we derive concentration inequalities for the empirical absolute moments of square symmetric matrices with independent symmetrically distributed +/-1 entries. Most of the previous results of this type are limited to…
Can the behavior of a random matrix be improved by modifying a small fraction of its entries? Consider a random matrix $A$ with i.i.d. entries. We show that the operator norm of $A$ can be reduced to the optimal order $O(\sqrt{n})$ by…
The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue of some non necessarily Gaussian complex Deformed Wigner Ensembles. The real model is also considered. Our approach is close to the one…
A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…
We show that the distribution of (a suitable rescaling of) a single eigenvalue gap $\lambda_{i+1}(M_n)-\lambda_i(M_n)$ of a random Wigner matrix ensemble in the bulk is asymptotically given by the Gaudin-Mehta distribution, if the Wigner…
Relationships are obtained expressing the breaking of spin-reversal symmetry by an external magnetic field in Gibbsian canonical equilibrium states of spin systems under specific assumptions. These relationships include an exact fluctuation…