© 2015

Random Walks, Random Fields, and Disordered Systems

  • Marek Biskup
  • Jiří Černý
  • Roman Kotecký

Part of the Lecture Notes in Mathematics book series (LNM, volume 2144)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Amin Coja-Oghlan
    Pages 117-146
  3. Gregory F. Lawler, Jacob Perlman
    Pages 211-235
  4. Back Matter
    Pages 237-242

About this book


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.


60J85;60K35;60K05;82D30;82B28;82B41;05D40;82B26. Cavity Method Disordered System Loop-Soup Model Random Fields Random Walk

Authors and affiliations

  1. 1.Inst. for Applied MathematicsUniversity of BonnBonnGermany
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Mathematics InstituteGoethe UniversityFrankfurtGermany
  4. 4.Faculty of Industrial Engineering and MaTechnion -Israel Institute of TechnologyHaifaIsrael
  5. 5.Department of MathematicsUniversity of ChicagoChicagoUSA

Editors and affiliations

  • Marek Biskup
    • 1
  • Jiří Černý
    • 2
  • Roman Kotecký
    • 3
  1. 1.Department of MathematicsUniversity of California in Los AngelesLos AngelesUSA
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria
  3. 3.Department of MathematicsUniversity of WarwickWarwickUnited Kingdom

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