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We present preprocessing-MPC schemes of arithmetic functions with optimal round complexity, function-independent correlated randomness, and communication and space complexities that grow linearly with...
We are delighted to organize and host the second edition of the biennial Summer School on Random Matrices at the University of Michigan during June 18--29, 2018.We thank the Michigan Center for Applie...
What is...a Random Matrix?     Random Matrix       2015/7/8
What is...a Random Matrix
We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed o...
This paper proposes a CLT for linear spectral statistics of random matrix $S^{-1}T$ for a general non-negative definite and {\bf non-random} Hermitian matrix $T$.
Using Random Matrix Theory, we build a covariance matrix between stocks of the BM&F-Bovespa (Bolsa de Valores, Mercadorias e Futuros de S\~ao Paulo) which is cleaned of some of the noise due to the co...
We study the cross-correlation matrix $C_{ij}$ of inventory variations of the most active individual and institutional investors in an emerging market to understand the dynamics of inventory variation...
Abstract: We propose a random matrix model for families of elliptic curve L-functions of finite conductor. A repulsion of their critical zeros away from the center of the critical strip was observed b...
We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe general ideas a...
Abstract: We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe gener...
In array processing, a common problem is to estimate the angles of arrival of $K$ deterministic sources impinging on an array of $M$ antennas, from $N$ observations of the source signal, corrupted by ...
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain e...
Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov ...
We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorith...
We consider a structural model for the estimation of credit risk based on Merton's original model. By using Random-Matrix theory we demonstrate analytically that the presence of correlations severely ...

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