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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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Estimating Factor-Based Spot Volatility Matrices with Noisy and Asynchronous High-Frequency Data
噪声 异步高频 数据估算 因子 现货波动率 矩阵
2023/5/4
With noisy and asynchronous high-frequency data collected for an ultra-large number of assets, we estimate high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure. A loca...
On positive definite preserving linear transformations of rank $r$ on real symmetric matrices
positive definite linear transformations
2010/11/22
We study on what conditions on $B_k,$ \ a linear transformation of rank $r$ \label{form} T(A)=\sum_{k=1}^r\tr(AB_k)U_k where $U_k,\ k=1,2,..., r$ are linear independent and all positive definite; is p...
Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case
Double scaling limits minimal (2m,1) models random matrices
2010/4/2
In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the int...
On Weighted Partial Orderings on the Set of Rectangular Complex Matrices
Weighted partial ordering Matrix function Singular value ecomposition
2010/1/22
In this paper, the relations between the weighted partial orderings on the set of rectangular complex matrices are first studied. Then, using the matrix function defined by Yang and Li [H. Yang and H....
Multiplicative Principal-Minor Inequalities for A Class of Oscillatory Matrices
Totally positive matrices Determinant Principal minor Bidiagonal factorization Determinantal inequalities Generators
2010/1/22
A square matrix is said to be totally nonnegative (respectively, positive) if all of its minors are nonnegative (respectively, positive). Determinantal inequalities have been a popular and important ...
Suppose $\mathbf{F}$ is a field different from $\mathbf{F}_{2},$ the field with two elements. Let $M_{n}(\mathbf{F})$ and $S_{n}(\mathbf{{F})}$ be the space of $n\times n$ full matrices and the spac...
THE GEOMETRIC PROPERTIES OF THE SET OF LYAPUNOV MATRICES AND THE STABILITY OF THE MATRIX FAMILY
Stability Matrix family Lyapunov equat
2007/8/7
Given a stable matrix A∈C~(n×n), there are some simple simultaneous inequalities whose coefficients rely on A. For \forall P~H=P∈C~(n×n), if P satisfies these inequlities, then PA+A~HP<0. As anapplica...
ON THE \ellP NORMS OF ALMOST CAUCHY-TOEPLITZ MATRICES
Cauchy Toeplitz norm Cauchy-Toeplitz matrix matrix norm
2010/3/17
In this study, we have given the definition of almost Cauchy-Toeplitz matrix. i.e. its elements are tij= a(i=j) and tij=1/(i-j)\, (i\neq j) such that a is a real number. We have found a lower and uppe...