---

＜電子ブック＞
Random Walks, Random Fields, and Disordered Systems / by Anton Bovier, David Brydges, Amin Coja-Oghlan, Dmitry Ioffe, Gregory F. Lawler ; edited by Marek Biskup, Jiří Černý, Roman Kotecký
(Lecture Notes in Mathematics. ISSN:16179692 ; 2144)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XIII, 239 p. 14 illus., 3 illus. in color : online resource
著者標目	*Bovier, Anton author Brydges, David author Coja-Oghlan, Amin author Ioffe, Dmitry author Lawler, Gregory F author Biskup, Marek editor Černý, Jiří editor Kotecký, Roman editor SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Condensed matter LCSH:Computer science—Mathematics LCSH:Mathematical statistics LCSH:Discrete mathematics LCSH:Probabilities FREE:Mathematical Physics FREE:Phase Transitions and Multiphase Systems FREE:Probability and Statistics in Computer Science FREE:Discrete Mathematics FREE:Probability Theory
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-19339-7

 類似資料