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Author : John M. Noble
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (258 download)
Download or read book The Directed Polymer in a Random Environment written by John M. Noble and published by . This book was released on 1996 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Francis Comets
Publisher : Springer
ISBN 13 : 3319504878
Total Pages : 210 pages
Book Rating : 4.3/5 (195 download)
Download or read book Directed Polymers in Random Environments written by Francis Comets and published by Springer. This book was released on 2017-01-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Author : Carles Rovira
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (897 download)
Download or read book On the Brownian Directed Polymer in a Gaussian Random Environment written by Carles Rovira and published by . This book was released on 2004 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank den Hollander
Publisher : Springer
ISBN 13 : 3642003338
Total Pages : 271 pages
Book Rating : 4.6/5 (42 download)
Download or read book Random Polymers written by Frank den Hollander and published by Springer. This book was released on 2009-04-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.
Author : Vu-Lan Nguyen
Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.:/5 (993 download)
Download or read book Directed Polymers in Random Media written by Vu-Lan Nguyen and published by . This book was released on 2016 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis focuses on (mostly 1 + 1 dimensional) directed polymers in random media. These are classical and celebrated models in the statistical mechanics of disordered systems and describe a one dimensional interface interacting with a d + 1-dimensional random environment where it is immersed. A very important question is to understand, in the limit where the polymer's length tends to infinity and for a typical realization of the environment, the geometric properties of the polymer: typical transversal displacement of the endpoint and its fluctuations, polymer localization at strong disorder around typical tubes determined by disorder... A strictly related problem of great interest is to study the fluctuations of the free energy. The main focus is on the so-called log-gamma polymer. This model, introduced by Seppalainen, is obtained by making a specific choice for the disorder law: the random variables are inverse Gamma variables. For this specific disorder choice, he proved that the variance of the log of the partition function is of order N"2/3, as expected by KPZ theory. This was refined into a full limit theorem Tracy -Widom type fluctuations) by Corwin, O'Connell, Seppalainen and Zygouras, via an explicit formula for the Laplace transform of a single partition function. It was until now an open problem to compute correlations between partition functions with different end-points and to study the asymptotic distribution of the polymer's endpoint. The present thesis addresses, among others, these two very challenging problems. On the other hand, we consider applications of stochastic orders on the study of directed polymer and disordered systems.
Author : Alain-Sol Sznitman
Publisher : Springer Science & Business Media
ISBN 13 : 3662112817
Total Pages : 366 pages
Book Rating : 4.6/5 (621 download)
Download or read book Brownian Motion, Obstacles and Random Media written by Alain-Sol Sznitman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.
Author : Zi Sheng Feng
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)
Download or read book Rescaled Directed Random Polymer in Random Environment in Dimension 1+2 written by Zi Sheng Feng and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Dominique Deuschel
Publisher : Springer Science & Business Media
ISBN 13 : 3642238114
Total Pages : 518 pages
Book Rating : 4.6/5 (422 download)
Download or read book Probability in Complex Physical Systems written by Jean-Dominique Deuschel and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.
Author : Abolfazl Bayat
Publisher : Springer Nature
ISBN 13 : 303103998X
Total Pages : 549 pages
Book Rating : 4.0/5 (31 download)
Download or read book Entanglement in Spin Chains written by Abolfazl Bayat and published by Springer Nature. This book was released on 2022-09-26 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.
Author : Firas Rassoul-Agha
Publisher : American Mathematical Soc.
ISBN 13 : 0821875787
Total Pages : 335 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Course on Large Deviations with an Introduction to Gibbs Measures written by Firas Rassoul-Agha and published by American Mathematical Soc.. This book was released on 2015-03-12 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course. The book begins with a straightforward approach to the key ideas and results of large deviation theory in the context of independent identically distributed random variables. This includes Cramér's theorem, relative entropy, Sanov's theorem, process level large deviations, convex duality, and change of measure arguments. Dependence is introduced through the interactions potentials of equilibrium statistical mechanics. The phase transition of the Ising model is proved in two different ways: first in the classical way with the Peierls argument, Dobrushin's uniqueness condition, and correlation inequalities and then a second time through the percolation approach. Beyond the large deviations of independent variables and Gibbs measures, later parts of the book treat large deviations of Markov chains, the Gärtner-Ellis theorem, and a large deviation theorem of Baxter and Jain that is then applied to a nonstationary process and a random walk in a dynamical random environment. The book has been used with students from mathematics, statistics, engineering, and the sciences and has been written for a broad audience with advanced technical training. Appendixes review basic material from analysis and probability theory and also prove some of the technical results used in the text.
Author : Arne Jensen
Publisher : World Scientific
ISBN 13 : 9814449245
Total Pages : 743 pages
Book Rating : 4.8/5 (144 download)
Download or read book XVIIth International Congress on Mathematical Physics written by Arne Jensen and published by World Scientific. This book was released on 2014 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.
Author : Lester N. Coyle
Publisher :
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.3/5 (91 download)
Download or read book Diffusion of Random Walk in a Random Environment written by Lester N. Coyle and published by . This book was released on 1995 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giambattista Giacomin
Publisher : World Scientific
ISBN 13 : 1908979267
Total Pages : 259 pages
Book Rating : 4.9/5 (89 download)
Download or read book Random Polymer Models written by Giambattista Giacomin and published by World Scientific. This book was released on 2007-03-22 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials.This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models./a
Author : Ishwar V. Basawa
Publisher : IMS
ISBN 13 : 9780940600256
Total Pages : 294 pages
Book Rating : 4.6/5 (2 download)
Download or read book Selected Proceedings of the Sheffield Symposium on Applied Probability written by Ishwar V. Basawa and published by IMS. This book was released on 1991 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Véronique Gayrard
Publisher : Springer
ISBN 13 : 3319176749
Total Pages : 213 pages
Book Rating : 4.3/5 (191 download)
Download or read book Correlated Random Systems: Five Different Methods written by Véronique Gayrard and published by Springer. This book was released on 2015-06-09 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.
Author : Giambattista Giacomin
Publisher : Springer Science & Business Media
ISBN 13 : 3642211550
Total Pages : 140 pages
Book Rating : 4.6/5 (422 download)
Download or read book Disorder and Critical Phenomena Through Basic Probability Models written by Giambattista Giacomin and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians.
Author : René Carmona
Publisher : American Mathematical Soc.
ISBN 13 : 9780821808061
Total Pages : 360 pages
Book Rating : 4.8/5 (8 download)
Download or read book Stochastic Partial Differential Equations: Six Perspectives written by René Carmona and published by American Mathematical Soc.. This book was released on 1999 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR
