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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Branching random walks driven by products of random matrices
随机矩阵 乘积驱动 分支随机 游走
2023/4/18
A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Products of random matrices
随机矩阵 乘积 极限定理收敛率
2023/4/19
Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random matrices of type $d \times d $ with real coefficients. Consider the products $G_n : = g_n \ldots g_1$ and the rand...
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 Eigenvalues of Random Matrices.
Linear Functionals of Eigenvalues of Random Matrices
Random unitary matrix the calculation function
2015/7/14
.L.et 1% be a random r~x r~unitary matrix with distribution given
by Haar measure on the unitary group. Using explicit monlerlt calculations,
a general criterion is given for linear cornbinations of...
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。
Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices
Finite-state channel hidden Markov model random matrices Shannon capacity
2015/7/6
The finite-state Markov channel (FSMC) is a timevarying channel having states that are characterized by a finitestate Markov chain. These channels have infinite memory, which complicates their capacit...
Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
Random Matrix Theory characteristic roots largest eigenvalue Tracy-Widom Distribution Wishart Matrices Gaussian Orthogonal Ensemble
2012/11/23
We derive the exact distribution of the largest eigenvalue for finite dimensions real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). We compare the exact distribution with the Tracy-...
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...
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
Freezing Transition Characteristic Polynomials Random Matrices the Riemann Zeta-Function
2012/2/24
We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus...
On High Moments and the Spectral Norm of Large Dilute Wigner Random Matrices
random matrices Wigner ensemble dilute random matrices
2011/9/22
Abstract: We consider a dilute version of the Wigner ensemble of n-dimensional random matrices H such that each row has in average \rho_n non-zero elements. We study asymptotic properties of the spect...
Induced Ginibre ensemble of random matrices and quantum operations
Induced Ginibre ensemble random matrices quantum operations
2011/9/20
Abstract: A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matri...
A CLT for Information-theoretic statistics of Non-centered Gram random matrices
Random Matrix Spectral measure Stieltjes Transform
2011/7/19
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^{1/2} X_n...
A Subspace Estimator for Fixed Rank Perturbations of Large Random Matrices
Large Random Matrix Theory MUSIC Algorithm Extreme Eigenvalues
2011/7/6
This paper deals with the problem of parameter estimation based on certain eigenspaces of the empirical covariance matrix of an observed multidimensional time series, in the case where the time series...