E-Book Overview
This book is drawn from the recent literature on the asymptotic behavior of random permanents and random matchings. In particular, the authors present an elegant connection between the problem of an asymptotic behavior for a certain family of functionals on random matrices and the asymptotic results in the classical theory of the so-called U-statistics -- objects of fundamental importance in the non-parametric statistical inference.
This book is self-contained and accessible to any mathematics, statistics or engineering graduate student who has taken basic introductory courses in probability theory and mathematical statistics.
Dr.Grzegorz A. Rempala is a Professor of Statistics in the Department of Mathematics at the University of Louisville in Louisville, KY. Dr. Jacek Wesolowski is a Professor of Mathematics and Associate Dean for Research at the Faculty of Mathematics and Information Science, Warsaw University of Technology in Warsaw, Poland.
The volume is a result of the authors’ collaborative effort initiated at the IMA during the Institute's 2003/04 annual program on "Probability and Statistics in Complex Systems: Genomics, Networks, and Finance Engineering".
E-Book Content
The IMA Volumes in Mathematics and its Applications Volume 147
Series Editors Douglas N. Arnold Arnd Scheel
Institute for Mathematics and its Applications (IMA) The Institute for Mathematics and its Applications was established by a grant from the National Science Foundation to the University of Minnesota in 1982. The primary mission of the IMA is to foster research of a truly interdisciplinary nature, establishing links between mathematics of the highest caliber and important scientific and technological problems from other disciplines and industries. To this end, the IMA organizes a wide variety of programs, ranging from short intense workshops in areas of exceptional interest and opportunity to extensive thematic programs lasting a year. IMA Volumes are used to communicate results of these programs that we believe are of particular value to the broader scientific community. The full list of IMA books can be found at the Web site of the Institute for Mathematics and its Applications: http://www.ima.umn.edu/springer/volumes.html Presentation materials from the IMA talks are available at http://www.ima.umn.edu/talks/ Douglas N. Arnold, Director of the IMA * * * * * * * * * *
IMA ANNUAL PROGRAMS 1982–1983 1983–1984 1984–1985 1985–1986 1986–1987 1987–1988 1988–1989 1989–1990 1990–1991 1991–1992 1992–1993 1993–1994 1994–1995 1995–1996 1996–1997
Statistical and Continuum Approaches to Phase Transition Mathematical Models for the Economics of Decentralized Resource Allocation Continuum Physics and Partial Differential Equations Stochastic Differential Equations and Their Applications Scientific Computation Applied Combinatorics Nonlinear Waves Dynamical Systems and Their Applications Phase Transitions and Free Boundaries Applied Linear Algebra Control Theory and its Applications Emerging Applications of Probability Waves and Scattering Mathematical Methods in Material Science Mathematics of High Performance Computing
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Grzegorz A. Rempała
Jacek Wesołowski
Authors
Symmetric Functionals on Random Matrices and Random Matchings Problems
123
Grzegorz A. Rempała Department of Mathematics University of Louisville, KY, USA Louisville 40292 http://www.louisville.edu/∼garemp01
ISBN: 978-0-387-75145-0
Jacek Wesołowski Wydzial Matematyki i Nauk Informacyjnych Politechnika Warszawska, Warszawa, 1 Pl. Politechniki Warszawa 00-661 Poland
e-ISBN: 970-0-387-75146-7
Mathematics Subject Classification (2000): 60F05, 60F17, 62G20, 62G10, 05A16 Library of Congress Control Number: 2007938212 c 2008