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Random Walks, Random Fields, and Disordered Systems

✍ Scribed by Anton Bovier, David Brydges, Amin Coja-Oghlan, Dmitry Ioffe, Gregory F. Lawler (auth.), Marek Biskup, Jiří Černý, Roman Kotecký (eds.)


Publisher
Springer International Publishing
Year
2015
Tongue
English
Leaves
254
Series
Lecture Notes in Mathematics 2144
Edition
1
Category
Library

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✦ Synopsis


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


Front Matter....Pages i-xiii
From Spin Glasses to Branching Brownian Motion—and Back?....Pages 1-64
The Renormalization Group and Self-avoiding Walk....Pages 65-116
Phase Transitions in Discrete Structures....Pages 117-146
Multidimensional Random Polymers: A Renewal Approach....Pages 147-210
Loop Measures and the Gaussian Free Field....Pages 211-235
Back Matter....Pages 237-242

✦ Subjects


Mathematical Physics; Phase Transitions and Multiphase Systems; Probability and Statistics in Computer Science; Discrete Mathematics; Probability Theory and Stochastic Processes


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