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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
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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
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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
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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...
Eigenvalues of products of unitary matrices and Lagrangian involutions
Unitary representations Parabolic bundles Lagrangian involutions
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2015/12/17
This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a puncturedsphere with fixedlocal monodromy. The submanifoldis definedvia products of inv...
On the construction of normal mixed difference matrices
On the construction normal mixed difference matrices
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2015/3/20
On the construction of normal mixed difference matrices.
Thin Hessenberg Pairs and Double Vandermonde Matrices
Leonard pair Hessenberg pair Vandermonde matrix
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2011/9/21
Abstract: A square matrix is called {\it Hessenberg} whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. Let $V$ denote a nonzero finite-dimensional vector ...
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
Toda Lattices Continuum Limit Random Matrices Odd Weights
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2011/7/7
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an inves...
Completely positive mappings and mean matrices
Matrix monotone function matrix means Hadamard product com-pletely positive mapping
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2011/2/24
Some functions f : R+ → R+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover,such a function f can define linear mapping...
The automorphism group of the group of unitriangular matrices over a field
automorphism group group of unitriangular matrices
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2011/2/28
This paper finds the generators of the automorphism group of the group of unitriangular matrices over a field. Most of this paper is an exposition of the work of V.M. Lev˘chuk, part of which is i...
The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices
The q-Gelfand-Tsetlin graph Gibbs measures
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2010/11/12
The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive...
Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields
Relatively Prime Polynomials Nonsingular Hankel Matrices
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2010/11/12
The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel ma...
Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
Cyclotomic Matrices Graphs imaginary quadratic fields
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2010/11/18
We determine all Hermitian $\mathcal{O}_{\Q(\sqrt{d})}$-matrices for which every eigenvalue is in the interval [-2,2], for each d in {-2,-7,-11,-15\}. To do so, we generalise charged signed graphs to...
On positive definite preserving linear transformations of rank $r$ on real symmetric matrices
positive definite linear transformations
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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...
A complete algorithm for determining copositive matrices
A complete algorithm for determining copositive matrices math
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2010/11/15
In this paper, we present a complete algorithm called COPOMATRIX for determining the copositivity of an $n\times n$ matrix. The core of this algorithm is decomposition theorem, which is used to deal ...
Inner Automorphisms of Lie Algebras Related with Generic 2 x 2 Matrices
free Lie algebras generic matrices inner automorphisms
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2010/12/13
Let Fm = Fm(varsl2(K)) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl2(K) over a field K of characteristic 0.