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Sharp Estimate (sharp + estimate)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Smallest singular value of a random rectangular matrix

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2009
Mark Rudelson
We prove an optimal estimate of the smallest singular value of a random sub-Gaussian matrix, valid for all dimensions. For an N × n matrix A with independent and identically distributed sub-Gaussian entries, the smallest singular value of A is at least of the order ,N , ,n , 1 with high probability. A sharp estimate on the probability is also obtained. © 2009 Wiley Periodicals, Inc. [source]

Linear stability and instability of relativistic Vlasov-Maxwell systems

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2007
Zhiwu Lin
We consider the linear stability problem for a symmetric equilibrium of the relativistic Vlasov-Maxwell (RVM) system. For an equilibrium whose distribution function depends monotonically on the particle energy, we obtain a sharp linear stability criterion. The growing mode is proved to be purely growing, and we get a sharp estimate of the maximal growth rate. In this paper we specifically treat the periodic 1½D case and the 3D whole-space case with cylindrical symmetry. We explicitly illustrate, using the linear stability criterion in the 1½D case, several stable and unstable examples. © 2006 Wiley Periodicals, Inc. [source]

Estimates of difference norms for functions in anisotropic Sobolev spaces

MATHEMATISCHE NACHRICHTEN, Issue 1 2004
V. I. Kolyada
Abstract We investigate the spaces of functions on ,n for which the generalized partial derivatives Dkf exist and belong to different Lorentz spaces L . For the functions in these spaces, the sharp estimates of the Besov type norms are found. The methods used in the paper are based on estimates of non-increasing rearrangements. These methods enable us to cover also the case when some of the pk's are equal to 1. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Right order spectral gap estimates for generating sets of ,4

RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2002
Matthias Löwe
Abstract Using coupling arguments, a distance method and Zeifman's method we give sharp estimates on the spectral gap for a special case of the class of Markov chains on generating n -tuples of Abelian groups. In our case the group is ,4. © 2002 Wiley Periodicals, Inc. Random Struct. Alg. 20: 220,238, 2002 [source]