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École d'Été de Probabilités de Saint-Flour

The Lace Expansion and its Applications

Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004

Authors: Slade, Gordon

Editors: Picard, Jean (Ed.)

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About this book

The lace expansion is a powerful and flexible method for understanding the critical scaling  of several models of interest in probability, statistical mechanics,
and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models.  Results include proofs of existence of critical exponents and construction of scaling limits. Often, the scaling limit is described in terms of super-Brownian motion.

About the authors

Gordon Slade is Professor at the University of British Columbia since 1999. Before he was Lecturer at the University of Virginia from 1985 to 1986 and  Professor at the McMaster University from 1986 to 1999. The Author has been awarded the UBC Killam Research Prize (Senior Science Category) in 2004 and the Prix de l'Institut Henri Poincaré--with Remco van der Hofstad--in2003. In 2003 he was Stieltjes Visiting Professor, in 1995 Coxeter-James Lecturer for the Canadian Mathematical Society. Since 2000 he is Fellow of the Royal Society of Canada. 

Reviews

From the reviews:

"The book consists mainly of materials for an advanced master course. … The book focusses on the modeling of mechanics, where the concept of a model shall be understood in its broadest sense, namely as a mathematical structure which describes mechanical phenomena. … A list of notations and an index are helpful to the reader. The little book with about 200 pages tackles many theories and concepts, without going much into detail." (Albrecht Bertram, Zentralblatt MATH, Vol. 1115 (17), 2007)

"This work is based on the author’s lectures on the lace expansion and its applications … . It contains the recent developments in the analysis of the lace expansion and the scaling limits of the critical objects discovered since the publication … . It also contains further applications of the lace expansion to other models and an extensive list of references. … The subject is still growing, and studying the lecture notes by Slade is a good starting point to learn the subject." (Akira Sakai, Mathematical Reviews, Issue 2007 m)


Table of contents (17 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-35518-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-31189-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Lace Expansion and its Applications
Book Subtitle
Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004
Authors
Editors
  • Jean Picard
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
1879
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-35518-2
DOI
10.1007/b128444
Softcover ISBN
978-3-540-31189-8
Series ISSN
0721-5363
Edition Number
1
Number of Pages
XIII, 233
Topics