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Random Walks, Random Fields, and Disordered Systems

Marek Biskup, Jiří Černý, Roman Kotecký (Herausgeber)

Anton Bovier, David Brydges, Amin Coja-Oghlan, Dmitry Ioffe, Gregory F. Lawler (Autoren)

Buch | Softcover

XIII, 239 Seiten

2015 | 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-19338-0 (ISBN)

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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.

Anton Bovier: From spin glasses to branching Brownian motion - and back?.- David Brydges: The Renormalization Group and Self-AvoidingWalk.- Amin Coja-Oghlan: Phase Transitions in Discrete Structures.- Dmitry Ioffe: Multidimensional Random Polymers : A Renewal Approach.- Gregory F. Lawler and Jacob Perlman: Loop measures and the Gaussian free field.

Erscheint lt. Verlag	29.9.2015
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIII, 239 p. 14 illus., 3 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	05D40 • 60J85 • 60J85;60K35;60K05;82D30;82B28;82B41;05D40;82B26. • 60K05 • 60K35 • 82B26. • 82B28 • 82B41 • 82D30 • Cavity Method • disordered system • Loop-Soup Model • random fields • Random Walk
ISBN-10	3-319-19338-4 / 3319193384
ISBN-13	978-3-319-19338-0 / 9783319193380
Zustand	Neuware