相关论文: Limiting Spectral Distribution of High-dimensional…

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…

We study harmonic chains with i.i.d. random spring constants $K_n$ and i.i.d. random masses $m_n$. We introduce a new combinatorial approach which allows to derive a compact approximate expression for the complex Lyapunov exponent, in terms…

We consider Erd\H{o}s-R\'{e}nyi graphs $G(n,p_n)$ with large constant expected degree $\lambda$ and $p_n=\lambda/n$. Bordenave and Lelarge (2010) showed that the infinite-volume limit, in the Benjamini-Schramm topology, is a Galton-Watson…

In this paper we find spectral properties in the large $N$ limit of Dirac operators that come from random finite noncommutative geometries. In particular for a Gaussian potential the limiting eigenvalue spectrum is shown to be universal…

High-dimensional sample correlation matrices are a crucial class of random matrices in multivariate statistical analysis. The central limit theorem (CLT) provides a theoretical foundation for statistical inference. In this paper, assuming…

Consider the sequence of continued fraction convergents $p_n/q_n$ to a random irrational number. We study the distribution of the sequences $p_n \pmod{m}$ and $q_n \pmod{m}$ with a fixed modulus $m$, and more generally, the distribution of…

In this work, we study the spectral statistics for Anderson model on $\ell^2(\mathbb{N})$ with decaying randomness whose single site distribution has unbounded support. Here we consider the operator $H^\omega$ given by $(H^\omega…

In random matrix theory, Marchenko-Pastur law states that random matrices with independent and identically distributed entries have a universal asymptotic eigenvalue distribution under large dimension limit, regardless of the choice of…

Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are…

We consider a self-similar phase space with specific fractal dimension $d$ being distributed with spectrum function $f(d)$. Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the…

In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…

Let $X_N$ be an $N\ts N$ random symmetric matrix with independent equidistributed entries. If the law $P$ of the entries has a finite second moment, it was shown by Wigner \cite{wigner} that the empirical distribution of the eigenvalues of…

Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$…

Electron Backscatter Diffraction (EBSD) is a technique to obtain microcrystallographic information from materials by collecting large-angle Kikuchi patterns in the scanning electron microscope (SEM). An important fundamental question…

Kipnis and Varadhan showed that for an additive functional, $S_n$ say, of a reversible Markov chain the condition $E(S_n^{2})/n \to \kappa \in (0,\infty)$ implies the convergence of the conditional distribution of $S_n/\sqrt{E(S_n^{2}})$,…

We present a steepest descent calculation of the Kallen-Lehmann spectral density of two-point functions involving complex conjugate masses in Euclidean space. This problem occurs in studies of (gauge) theories with Gribov-like propagators.…

We consider the complex eigenvalues of a Wishart type random matrix model $X=X_1 X_2^*$, where two rectangular complex Ginibre matrices $X_{1,2}$ of size $N\times (N+\nu)$ are correlated through a non-Hermiticity parameter $\tau\in[0,1]$.…

Let \{$X_{ij}$\}, $i,j=...,$ be a double array of i.i.d. complex random variables with $EX_{11}=0,E|X_{11}|^2=1$ and $E|X_{11}|^4<\infty$, and let $A_n=\frac{1}{N}T_n^{{1}/{2}}X_nX_n^*T_n^{{1}/{2}}$, where $T_n^{{1}/{2}}$ is the square root…

Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some…

Determinantal Point Processes (DPPs), which originate from quantum and statistical physics, are known for modelling diversity. Recent research [Ghosh and Rigollet (2020)] has demonstrated that certain matrix-valued $U$-statistics (that are…