Random walks, random fields, and disordered systems / Anton Bovier...[et al.].

Includes bibliographical references and index.

From Spin Glasses to Branching Brownian Motion--and Back? --
The Renormalization Group and Self-avoiding Walk --
Phase Transitions in Discrete Structures --
Multidimensional Random Polymers: A Renewal Approach --
Loop Measures and the Gaussian Free Field--
References--
Index.

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.