Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Probabilistic Combinatorics and Its Applications
 
Edited by: Béla Bollobás University of Memphis, Memphis, TN
Probabilistic Combinatorics and Its Applications
Hardcover ISBN:  978-0-8218-5500-3
Product Code:  PSAPM/44
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-0-8218-9259-6
Product Code:  PSAPM/44.E
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Hardcover ISBN:  978-0-8218-5500-3
eBook: ISBN:  978-0-8218-9259-6
Product Code:  PSAPM/44.B
List Price: $224.00 $174.50
MAA Member Price: $201.60 $157.05
AMS Member Price: $179.20 $139.60
Probabilistic Combinatorics and Its Applications
Click above image for expanded view
Probabilistic Combinatorics and Its Applications
Edited by: Béla Bollobás University of Memphis, Memphis, TN
Hardcover ISBN:  978-0-8218-5500-3
Product Code:  PSAPM/44
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
eBook ISBN:  978-0-8218-9259-6
Product Code:  PSAPM/44.E
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Hardcover ISBN:  978-0-8218-5500-3
eBook ISBN:  978-0-8218-9259-6
Product Code:  PSAPM/44.B
List Price: $224.00 $174.50
MAA Member Price: $201.60 $157.05
AMS Member Price: $179.20 $139.60
  • Book Details
     
     
    Proceedings of Symposia in Applied Mathematics
    Volume: 441991; 196 pp
    MSC: Primary 05; 68; 60; Secondary 52;

    Probabilistic methods have become a vital tool in the arsenal of every combinatorialist. The theory of random graphs is still a prime area for the use of probabilistic methods, and, over the years, these methods have also proved of paramount importance in many associated areas such as the design and analysis of computer algorithms. In recent years, probabilistic combinatorics has undergone revolutionary changes as the result of the appearance of some exciting new techniques such as martingale inequalities, discrete isoperimetric inequalities, Fourier analysis on groups, eigenvalue techniques, branching processes, and rapidly mixing Markov chains. The aim of this volume is to review briefly the classical results in the theory of random graphs and to present several of the important recent developments in probabilistic combinatorics, together with some applications.

    The first paper contains a brief introduction to the theory of random graphs. The second paper reviews explicit constructions of random-like graphs and discusses graphs having a variety of useful properties. Isoperimetric inequalities, of paramount importance in probabilistic combinatorics, are covered in the third paper. The chromatic number of random graphs is presented in the fourth paper, together with a beautiful inequality due to Janson and the important and powerful Stein-Chen method for Poisson approximation. The aim of the fifth paper is to present a number of powerful new methods for proving that a Markov chain is “rapidly mixing” and to survey various related questions, while the sixth paper looks at the same topic in a very different context. For the random walk on the cube, the convergence to the stable distribution is best analyzed through Fourier analysis; the final paper examines this topic and proceeds to several more sophisticated applications. Open problems can be found throughout each paper.

  • Table of Contents
     
     
    • Articles
    • Béla Bollobás — Random graphs [ MR 1141921 ]
    • Fan R. K. Chung — Constructing random-like graphs [ MR 1141922 ]
    • Imre Leader — Discrete isoperimetric inequalities [ MR 1141923 ]
    • Béla Bollobás — Random graphs revisited [ MR 1141924 ]
    • Umesh Vazirani — Rapidly mixing Markov chains [ MR 1141925 ]
    • Martin Dyer and Alan Frieze — Computing the volume of convex bodies: a case where randomness provably helps [ MR 1141926 ]
    • Persi Diaconis — Finite Fourier methods: access to tools [ MR 1141927 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 441991; 196 pp
MSC: Primary 05; 68; 60; Secondary 52;

Probabilistic methods have become a vital tool in the arsenal of every combinatorialist. The theory of random graphs is still a prime area for the use of probabilistic methods, and, over the years, these methods have also proved of paramount importance in many associated areas such as the design and analysis of computer algorithms. In recent years, probabilistic combinatorics has undergone revolutionary changes as the result of the appearance of some exciting new techniques such as martingale inequalities, discrete isoperimetric inequalities, Fourier analysis on groups, eigenvalue techniques, branching processes, and rapidly mixing Markov chains. The aim of this volume is to review briefly the classical results in the theory of random graphs and to present several of the important recent developments in probabilistic combinatorics, together with some applications.

The first paper contains a brief introduction to the theory of random graphs. The second paper reviews explicit constructions of random-like graphs and discusses graphs having a variety of useful properties. Isoperimetric inequalities, of paramount importance in probabilistic combinatorics, are covered in the third paper. The chromatic number of random graphs is presented in the fourth paper, together with a beautiful inequality due to Janson and the important and powerful Stein-Chen method for Poisson approximation. The aim of the fifth paper is to present a number of powerful new methods for proving that a Markov chain is “rapidly mixing” and to survey various related questions, while the sixth paper looks at the same topic in a very different context. For the random walk on the cube, the convergence to the stable distribution is best analyzed through Fourier analysis; the final paper examines this topic and proceeds to several more sophisticated applications. Open problems can be found throughout each paper.

  • Articles
  • Béla Bollobás — Random graphs [ MR 1141921 ]
  • Fan R. K. Chung — Constructing random-like graphs [ MR 1141922 ]
  • Imre Leader — Discrete isoperimetric inequalities [ MR 1141923 ]
  • Béla Bollobás — Random graphs revisited [ MR 1141924 ]
  • Umesh Vazirani — Rapidly mixing Markov chains [ MR 1141925 ]
  • Martin Dyer and Alan Frieze — Computing the volume of convex bodies: a case where randomness provably helps [ MR 1141926 ]
  • Persi Diaconis — Finite Fourier methods: access to tools [ MR 1141927 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.