Symmetric functionals on random matrices and random matchings problems /
Saved in:
| Imprint: | [New York] : Springer, c2008. |
|---|---|
| Description: | xiv, 179 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | IMA volumes in mathematics and its applications ; v. 147 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7187378 |
Table of Contents:
- Foreword
- Preface
- 1. Basic Concepts
- 1.1. Bipartite Graphs in Complex Stochastic Systems
- 1.2. Perfect Matchings
- 1.3. Permanent Function
- 1.4. U-statistics
- 1.5. The H-decomposition
- 1.6. P-statistics
- 1.7. Examples
- 1.8. Bibliographic Details
- 2. Properties of P-statistics
- 2.1. Preliminaries: Martingales
- 2.2. H-decomposition of a P-statistic
- 2.3. Variance Formula for a P-statistic
- 2.4. Bibliographic Details
- 3. Asymptotics for Random Permanents
- 3.1. Introduction
- 3.2. Preliminaries
- 3.2.1. Limit Theorems for Exchangeable Random Variables
- 3.2.2. Law of Large Numbers for Triangular Arrays
- 3.2.3. More on Elementary Symmetric Polynomials
- 3.3. Limit Theorem for Elementary Symmetric Polynomials
- 3.4. Limit Theorems for Random Permanents
- 3.5. Additional Central Limit Theorems
- 3.6. Strong Laws of Large Numbers
- 3.7. Bibliographic Details
- 4. Weak Convergence of Permanent Processes
- 4.1. Introduction
- 4.2. Weak Convergence in Metric Spaces
- 4.3. The Skorohod Space
- 4.4. Permanent Stochastic Process
- 4.5. Weak Convergence of Stochastic Integrals and Symmetric Polynomials Processes
- 4.6. Convergence of the Component Processes
- 4.7. Functional Limit Theorems
- 4.8. Bibliographic Details
- 5. Weak Convergence of P-statistics
- 5.1. Multiple Wiener-Ito Integral as a Limit Law for U-statistics
- 5.1.1. Multiple Wiener-Ito Integral of a Symmetric Function
- 5.1.2. Classical Limit Theorems for U-statistics
- 5.1.3. Dynkin-Mandelbaum Theorem
- 5.1.4. Limit Theorem for U-statistics of Increasing Order
- 5.2. Asymptotics for P-statistics
- 5.3. Examples
- 5.4. Bibliographic Details
- 6. Permanent Designs and Related Topics
- 6.1. Incomplete U-statistics
- 6.2. Permanent Design
- 6.3. Asymptotic properties of USPD
- 6.4. Minimal Rectangular Schemes
- 6.5. Existence and Construction of MRS
- 6.5.1. Strongly Regular Graphs
- 6.5.2. MRS and Orthogonal Latin Squares
- 6.6. Examples
- 6.7. Bibliographic Details
- 7. Products of Partial Sums and Wishart Determinants
- 7.1. Introduction
- 7.2. Products of Partial Sums for Sequences
- 7.2.1. Extension to Classical U-statistics
- 7.3. Products of Independent Partial Sums
- 7.3.1. Extensions
- 7.4. Asymptotics for Wishart Determinants
- 7.5. Bibliographic Details
- References
- Index
