Symmetric Functionals on Random Matrices and Random Matchings Problems

1. Front Matter

   Pages I-XIV

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2. Basic Concepts

   Pages 1-17

3. Properties of P-statistics

   Pages 19-33

4. Asymptotics for Random Permanents

   Pages 35-65

5. Weak Convergence of Permanent Processes

   Pages 67-86

6. Weak Convergence of P-statistics

   Pages 87-120

7. Permanent Designs and Related Topics

   Pages 121-148

8. Products of Partial Sums and Wishart Determinants

   Pages 149-169

9. Back Matter

   Pages 171-184

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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.

• Functionals
• Information
• Random
• Rempala
• STATISTICA
• Symmetric
• mathematical statistics

From the reviews:

"This monograph provides an account of recent research on questions related to asymptotics for random permanents and random matchings. … Each chapter finishes with a brief section on bibliographic details. These sections place the work in context providing references to key papers in the area as well as other sources of background information. The text is accessible to graduate students with a basic background in probability theory and statistics." (Neville Weber, Zentalblatt MATH, Vol. 1147, 2008)

• Department of Mathematics, University of Louisville, Louisville, USA

  Grzegorz A. Rempala

• Wydzial Matematyki i Nauk Informacyjnych, PolitechnikaWarszawska, Warszawa, Poland

  Jacek Wesolowski

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