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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.
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