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Month: February 2011

Concentration for empirical spectral distributions

I have just updated my former post on the concentration for empirical spectral distributions. Surprisingly, the concentration of empirical spectral distributions of random matrices around their mean holds under very weak assumptions (independent rows). No moments assumptions, no Poincaré or log-Sobolev inequalities, no Talagrand concentration inequalities for convex Lipschitz functions. The brave Azuma-Hoeffding-McDiarmid bounded differences inequalities  are enough!

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Computational Rough Paths [CoRoPa]

University of Oxford, United-Kingdom

CoRoPa stands for Computational Rough Paths.

http://coropa.sourceforge.net/

The aim of CoRoPa is to provide a software framework for various ideas related to Rough Path Theory, including rough differential equations and the digital description of serial data streams. The CoRoPa project results from a research programme led by Professor Terry J. Lyons. The intial C++ code was written by Terry and I with the support of the MathFIT/EPSRC-LMS grant GR/R2962/8/01 [HBKBU] and has been available for several years. Additional Matlab code was contributed later by Christophe Ladroue.

Recently, the code has been substantially updated and rewritten by Stephen Buckley, Greg Gyurkó, Christian Litterer, Terry Lyons, Arend Janssen, ChangLiang Xu.

Keywords: Rough Paths, Rough Differential Equation, Stochastic Analysis, Digital Description of Serial Data Streams, Signal Processing, Inverse Problems, Data Compression, Information Theory, Free (Lie) Algebras, Heisenberg Groups, Free Tensors, Polynomial Vector Fields.

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