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Optimal-Round Preprocessing-MPC via Polynomial Representation and Distributed Random Matrix (extended abstract)
MPC with preprocessing correlated randomness optimal round complexity
2019/9/16
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...
Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models
Integrable operators Riemann-Hilbert approach Deift-Zhou method asymptotical analysis of Fredholm determinants
2015/1/19
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...
CLT for linear spectral statistics of random matrix $S^{-1}T$
CLT linear spectral statistics random matrix $S^{-1}T$
2013/6/13
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 $T$.
Building portfolios of stocks in the Sao Paulo Stock Exchange using Random Matrix Theory
Building portfolios stocks the Sao Paulo Stock Exchange Random Matrix Theory
2012/3/2
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...
Random matrix approach to the dynamics of stock inventory variations
Random matrix approach dynamics stock inventory variations
2012/3/2
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...
A Random Matrix Model for Elliptic Curve $L$-Functions of Finite Conductor
Elliptic Curves Low Lying Zeros n-Level Statistics Random Matrix Theory Jacobi Ensembles Characteristic Polynomial
2011/9/19
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...
Random matrix approach in search for weak signals immersed in background noise
Random matrix approach search signals immersed background noise
2011/10/17
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...
Random matrix approach in search for weak signals immersed in background noise
Random matrix weak signals immerse background noise
2011/8/4
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...
Large information plus noise random matrix models and consistent subspace estimation in large sensor networks
Large information plus noise random matrix models consistent subspace estimation large sensor networks
2011/7/7
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 ...
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
multifractal dimensions Perturbation random matrix ensembles
2011/7/6
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...
Geometric sensitivity of random matrix results: consequences for shrinkage estimators of covariance and related statistical methods
random matrix related statistical shrinkage estimators
2011/6/16
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
...
Cross Correlation of Intra-day Stock Prices in Comparison to Random Matrix Theory
Principal Component Random Matrix Theory Cross Correlation Eigenvalues Stock Market
2013/1/28
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 ...