Random Walks, Random Fields, and Disordered Systems (Lecture Notes in Mathematics, Band 2144) - Softcover

Bovier, Anton; Brydges, David; Coja-Oghlan, Amin; Ioffe, Dmitry; Lawler, Gregory F.

Softcover

ISBN 10: 3319193384 ISBN 13: 9783319193380

Verlag: Springer, 2015

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Anton Bovier is Professor of Mathematics at the University of Bonn. His research concerns applications of probability theory in physics and biology, with a focus on statistical mechanics, metastability and ageing. He has published over 130 scientific papers, and a monograph on "Statistical Mechanics of Disordered Systems". He is a Fellow of the Institute for Mathematical Statistics. He is member of the Clusters of Excellence "Hausdorff Centre for Mathematics" and "ImmunoSensation", both at the University of Bonn. Frank den Hollander is Professor of Mathematics at Leiden University. His research focuses on probability theory, statistical physics, population dynamics and complex networks. He has published over 150 scientific papers, and two monographs on "Large Deviations" and "Random Polymers". He is a member of the Royal Dutch Academy of Sciences, and a Fellow of the American Mathematical Society and of the Institute of Mathematical Statistics. He is recipient of a 5-year Advanced Grant by the European Research Council and a 10-year consortium grant by the Dutch Ministry of Education, Culture and Science.

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2015
• Sprache: Englisch
• ISBN 10: 3319193384
• ISBN 13: 9783319193380
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 256
• Herausgeber: Biskup Marek, Černý Jiří, Kotecký Roman
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland