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Matrix Completion from Noisy Entries
matrix completion low-rank matrices spectral methods manifold optimization
2015/8/21
Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from colla...
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that...
Asymptotic expansion of beta matrix models in the one-cut regime
Asymptotic expansion beta matrix models the one-cut regime Probability
2011/8/26
Abstract: We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus,...
Pointwise stabilization of discrete-time matrix-valued stationary Markov chains
Markovian jump linear system pointwise stabilization random products of matrices
2011/8/22
Abstract: Let $(\Omega,\mathscr{F},\mathbb{P})$ be a probability space and $\bS=\{\mathrm{S}_1,...,\mathrm{S}_K\}$ a discrete-topological space that consists of $K$ real $d$-by-$d$ matrices, where $K$...
A Random Matrix Approach to VARMA Processes
VARMA random matrix theory free random variables Wishart ensemble covariance matrix historical estimation
2010/4/27
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit whe...
Trace Inequalities with Applications to Orthogonal Regression and Matrix Nearness Problems
Trace inequalities stochastic matrices orthogonal regression matrix nearness problems
2010/4/16
Matrix trace inequalities are finding increased use in many areas such as analysis, where they can be used to generalise several well known classical inequalities, and computational statistics, where ...