
Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices
We prove the Central Limit Theorem for finitedimensional vectors of lin...
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Generalized Four Moment Theorem and an Application to CLT for Spiked Eigenvalues of Largedimensional Covariance Matrices
We consider a more generalized spiked covariance matrix Σ, which is a ge...
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The conjugate gradient algorithm on wellconditioned Wishart matrices is almost deteriministic
We prove that the number of iterations required to solve a random positi...
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On the Theoretical Properties of the Exchange Algorithm
Exchange algorithm is one of the most popular extensions of MetropolisH...
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A Central Limit Theorem for Classical Multidimensional Scaling
Classical multidimensional scaling (CMDS) is a widely used method in man...
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Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
In this paper, we consider the separable covariance model, which plays a...
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A Robust Iterative Scheme for Symmetric Indefinite Systems
We propose a twolevel nested preconditioned iterative scheme for solvin...
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Universality for the conjugate gradient and MINRES algorithms on sample covariance matrices
We present a probabilistic analysis of two Krylov subspace methods for solving linear systems. We prove a central limit theorem for norms of the residual vectors that are produced by the conjugate gradient and MINRES algorithms when applied to a wide class of sample covariance matrices satisfying some standard moment conditions. The proof involves establishing a four moment theorem for the socalled spectral measure, implying, in particular, universality for the matrix produced by the Lanczos iteration. The central limit theorem then implies an almostdeterministic iteration count for the iterative methods in question.
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