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 -