Random Walks, Random Fields, and Disordered Systems
Authors: Bovier, A., Brydges, D., Coja-Oghlan, A., Ioffe, D., Lawler, G.F.
Editors: Biskup, Marek, Černý, Jiří, Kotecky, Roman (Eds.)
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- About this book
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Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.
- Table of contents (5 chapters)
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From Spin Glasses to Branching Brownian Motion—and Back?
Pages 1-64
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The Renormalization Group and Self-avoiding Walk
Pages 65-116
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Phase Transitions in Discrete Structures
Pages 117-146
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Multidimensional Random Polymers: A Renewal Approach
Pages 147-210
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Loop Measures and the Gaussian Free Field
Pages 211-235
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Random Walks, Random Fields, and Disordered Systems
- Authors
-
- Anton Bovier
- David Brydges
- Amin Coja-Oghlan
- Dmitry Ioffe
- Gregory F. Lawler
- Editors
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- Marek Biskup
- Jiří Černý
- Roman Kotecky
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 2144
- Copyright
- 2015
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-19339-7
- DOI
- 10.1007/978-3-319-19339-7
- Softcover ISBN
- 978-3-319-19338-0
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- XIII, 239
- Number of Illustrations
- 11 b/w illustrations, 3 illustrations in colour
- Topics
