EAN: 9783319193380

RANDOM WALKS RANDOM FIELDS AND DISORDERED SYSTE...

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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