TY  - BOOK
AU  - Bovier,Anton
AU  - Brydges,David
AU  - Coja-Oghlan,Amin
AU  - Ioffe,Dmitry
AU  - Lawler,Gregory F.
AU  - Biskup,Marek
AU  - Cerny,Jiri
AU  - Kotecky,Roman
TI  - Random walks, random fields, and disordered systems
T2  - Lecture notes in mathematics
SN  - 9783319193380
U1  - 519.282 23
PY  - 2015///
CY  - Switzerland
PB  - Springer
KW  - Random walks (Mathematics)
KW  - Brownian motion processes
KW  - Mathematical Physics.
N1  - 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
N2  - 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
ER  -