Symmetric Functionals on Random Matrices and Random Matchings Problems (eBook)

This superb explication of a complex subject presents the current state of the art of the mathematical theory of symmetric functionals on random matrices. It emphasizes its connection with the statistical non-parametric estimation theory. The book provides a detailed description of the approach of symmetric function decompositions to the asymptotic theory of symmetric functionals, including the classical theory of U-statistics. It also presents applications of the theory.

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This IMA Volume in Mathematics and its Applications SYMMETRIC FUNCTIONALS ON RANDOM MATRICES AND RANDOM MATCHINGS PROBLEMS During the academic year 2003-2004, the Institute for Mathematics and its Applications (IMA) held a thematic program on Probability and Stat- tics in Complex Systems. The program focused on large complex systems in which stochasticity plays a signi?cant role. Such systems are very diverse, and the IMA program emphasized systems as varied as the human genome, the internet, and world ?nancial markets. Although quite di?erent, these s- tems have features in common, such as multitudes of interconnecting parts and the availability of large amounts of high-dimensional noisy data. The programemphasized the development and application of common mathem- ical and computational techniques to model and analyze such systems. About 1,000 mathematicians, statisticians, scientists, and engineers participated in the IMA thematic program, including about 50 who were in residence at the IMA during much or all of the year. The present volume was born during the 2003-2004 thematic program at the IMA. The two authors were visitors to the IMA during the program year, withthe?rstauthorresidentforthe entiretenmonths. Thisvolumeisaresult of the authors' interactions at the IMA, and, especially their discussions with the many other program participants in the program and their involvement in the numerous tutorials, workshops,and seminars held during the year.