Gaussian Fluctuation for Smoothed Local Correlations in CUE

Smoothed Analysis of Gaussian Elimination

We present a smoothed analysis of Gaussian elimination, both with partial pivoting and without pivoting. Let A be any matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the ...

Gaussian fluctuation in random matrices.

Let N(L) be the number of eigenvalues, in an interval of length L, of a matrix chosen at random from the Gaussian Orthogonal, Unitary or Symplectic ensembles of N by N matrices, in the limit N → ∞. We prove that [N(L) − 〈N(L)〉]/√logL has a Gaussian distribution when L → ∞. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results ...

Smoothed universal correlations in the two - dimensional

Fluctuation-response relations for multitime correlations

We show that time-correlation functions of arbitrary order for any random variable in a statistical dynamical system can be calculated as higher-order response functions of the mean history of the variable. The response is to a "control term" added as a modification to the master equation for statistical distributions. The proof of the relations is based upon a variational characterization of t...

Smoothed Performance Guarantees for Local Search

We study popular local search and greedy algorithms for standard machine scheduling problems. The performance guarantee of these algorithms is well understood, but the worst-case lower bounds seem somewhat contrived and it is questionable whether they arise in practical applications. To find out how robust these bounds are, we study the algorithms in the framework of smoothed analysis, in which...