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2018随机矩阵与自由概率论研讨会（Workshop on Random Matrices and Free Probability Theory）
2018 随机矩阵与自由概率论 研讨会
2017/12/20
The workshop will explore large-N asymptotics of random matrices, in connection with the operator-algebra models of their limiting behavior that appear in free probability theory. The behavior or rand...
On the Permanents of Complements of the Direct Sum of identity Matrices
Complement, permanent magnet straight, identity matrix
2015/7/14
On the Permanents of Complements of the Direct Sum of identity Matrices.
On the Eigenvalues of Random Matrices.
Random Matrices, Magic Squares and Matching Polynomials
Random matrix the rubik's cube matching polynomial
2015/7/8
Random Matrices, Magic Squares and Matching Polynomials。
Random doubly stochastic tridiagonal matrices
Markov chain birth and death chain cuto phenomenon random matrix
2015/7/7
Random doubly stochastic tridiagonal matrices。
Local Eigenvalue Density for General MANOVA Matrices
MANOVA random matrix Jacobi ensemble Local density of eigenvalues
2012/7/9
We consider random $n\times n$ matrices of the form $(XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}$, where $X$ and $Y$ have independent entries with zero mean and variance one. These matrices are the natural ge...
Random matrices: Universality of local spectral statistics of non-Hermitian matrices
Random matrices non-Hermitian matrices Probability
2012/6/30
It is a classical 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 asymp...
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of...
Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Consensus consensus+innovations performance analysis random network convergence in probability exponential rate
2012/3/1
Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed infere...
Accuracy of empirical projections of high-dimensional Gaussian matrices
high-dimensional Gaussian matrices Probability
2011/9/22
Abstract: Let $epsilon\in\R^{M\times M}$ be a centered Gaussian matrix whose entries are independent with variance $\sigma^2$. The accuracy of reduced-rank projections of $X=C+epsilon$ with a determin...
The probability of rectangular unimodular matrices over $\F_q[x]$
Natural density unimodular matrices Riemann’s zeta function q-zeta function finite field polynomial ring
2011/9/13
Abstract: In this note, we compute the probability that a $k\times n$ matrix can be extended to an $n\times n$ invertible matrix over $\F_q[x]$, which turns out to be $(1-q^{k-n})(1-q^{k-1-n})...(1-q^...
New estimators of spectral distributions of Wigner matrices
Wigner matrices Stieltjes transform nonparametric estimate domain of attraction of normal law
2011/9/6
Abstract: We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performan...
A CLT for Information-theoretic statistics of Non-centered Gram random matrices
Random Matrix Spectral measure Stieltjes Transform Central Limit Theorem
2011/8/22
Abstract: In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n...
This paper is concerlled with the investigation of a twrvparametric linear stationary iterative method, called Modified Extrapolated Jacobi (MEJ) method, for solving linear systems Ax = b, where A is ...