Random Walks, Random Fields, and Disordered Systems

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

• Department of Mathematics, University of California in Los Angeles, Los Angeles, USA

  Marek Biskup

• Faculty of Mathematics, University of Vienna, Vienna, Austria

  Jiří Černý

• Department of Mathematics, University of Warwick, Warwick, United Kingdom

  Roman Kotecký

• Inst. for Applied Mathematics, University of Bonn, Bonn, Germany

  Anton Bovier

• Department of Mathematics, University of British Columbia, Vancouver, Canada

  David Brydges

• Mathematics Institute, Goethe University, Frankfurt, Germany

  Amin Coja-Oghlan

• Faculty of Industrial Engineering and Ma, Technion -Israel Institute of Technology, Haifa, Israel

  Dmitry Ioffe

• Department of Mathematics, University of Chicago, Chicago, USA

  Gregory F. Lawler

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