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Author : Alexei Borodin
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (796 download)
Download or read book Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimensions written by Alexei Borodin and published by . This book was released on 2012 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexei Borodin
Publisher :
ISBN 13 :
Total Pages : 73 pages
Book Rating : 4.:/5 (17 download)
Download or read book Free Energy Fluctuations for Directed Polymers in Random Media in 1+1 Dimension written by Alexei Borodin and published by . This book was released on 2012 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : Dae Han Kang
Publisher :
ISBN 13 :
Total Pages : 173 pages
Book Rating : 4.:/5 (19 download)
Download or read book Limiting Free Energy and Scaling Exponents for Directed Polymers with Inhomogeneous Parameters written by Dae Han Kang and published by . This book was released on 2019 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider directed polymer models where a fluctuating path is coupled with a random environment. Our focus is on the models with a random environment given by inhomogeneous parameters. We study the limiting free energy of fairly general inhomogeneous models. First, we derive the existence and basic properties of the limiting free energy for an asymptotically mean stationary model. Second, we apply our results to the exactly solvable log-gamma polymer. We give a variational formula for the point to point free energy in terms of the marginal distributions of the parameters. We identify critical angles at which the free energy transitions from strictly concave to linear. We also obtain explicit formulas for some special distributions of the parameters. Third, we study the fluctuation of free energy around some limit shape. We give scaling exponents for the log-gamma polymer. The KPZ exponent 1/3 appears in the concave sector and the diffusive exponent 1/2 in the flat region.
Author : Christian James Noack
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (18 download)
Download or read book Fluctuation Exponents and Exact Solvability of 1+1 Dimensional Directed Lattice Polymers written by Christian James Noack and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that the stationary point-to-point versions of the four 1+1 dimensional lattice directed polymers: the log-gamma, strict-weak, beta, and inverse-beta models all have the KPZ predicted free energy and path fluctuation exponents of 1/3 and 2/3 respectively. We do this in a uniform manner by first defining two types of integrability which the four models share, namely T^{h, Y} - invariance and the "Mellin transform property", and then showing that any model possessing these two forms of integrability has the KPZ predicted fluctuation exponents. T^{h, Y} -invariance encapsulates the stationarity of the four models, while the Mellin transform property says the model has sufficiently well-behaved or regular distributions. In addition, we show that under some regularity assumptions, up to natural modifications, there exist no other T^{h, Y} -invariant models beyond these four. We conclude by providing a partial connection between T^{h, Y} -invariance and a third form of integrability, namely coordinate Bethe ansatz solvability
Author : Percy Deift
Publisher : Cambridge University Press
ISBN 13 : 1107079926
Total Pages : 539 pages
Book Rating : 4.1/5 (7 download)
Download or read book Random Matrix Theory, Interacting Particle Systems and Integrable Systems written by Percy Deift and published by Cambridge University Press. This book was released on 2014-12-15 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles.
Author : Michael Damron
Publisher : American Mathematical Soc.
ISBN 13 : 1470435535
Total Pages : 256 pages
Book Rating : 4.4/5 (74 download)
Download or read book Random Growth Models written by Michael Damron and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Author : Giambattista Giacomin
Publisher : Springer
ISBN 13 : 3030150968
Total Pages : 649 pages
Book Rating : 4.0/5 (31 download)
Download or read book Stochastic Dynamics Out of Equilibrium written by Giambattista Giacomin and published by Springer. This book was released on 2019-06-30 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.
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 : Alejandro F. Ramírez
Publisher : Springer
ISBN 13 : 149390339X
Total Pages : 178 pages
Book Rating : 4.4/5 (939 download)
Download or read book Topics in Percolative and Disordered Systems written by Alejandro F. Ramírez and published by Springer. This book was released on 2014-06-16 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.
Author : Sourav Chatterjee
Publisher : Springer Science & Business Media
ISBN 13 : 3319038869
Total Pages : 156 pages
Book Rating : 4.3/5 (19 download)
Download or read book Superconcentration and Related Topics written by Sourav Chatterjee and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: A certain curious feature of random objects, introduced by the author as “super concentration,” and two related topics, “chaos” and “multiple valleys,” are highlighted in this book. Although super concentration has established itself as a recognized feature in a number of areas of probability theory in the last twenty years (under a variety of names), the author was the first to discover and explore its connections with chaos and multiple valleys. He achieves a substantial degree of simplification and clarity in the presentation of these findings by using the spectral approach. Understanding the fluctuations of random objects is one of the major goals of probability theory and a whole subfield of probability and analysis, called concentration of measure, is devoted to understanding these fluctuations. This subfield offers a range of tools for computing upper bounds on the orders of fluctuations of very complicated random variables. Usually, concentration of measure is useful when more direct problem-specific approaches fail; as a result, it has massively gained acceptance over the last forty years. And yet, there is a large class of problems in which classical concentration of measure produces suboptimal bounds on the order of fluctuations. Here lies the substantial contribution of this book, which developed from a set of six lectures the author first held at the Cornell Probability Summer School in July 2012. The book is interspersed with a sizable number of open problems for professional mathematicians as well as exercises for graduate students working in the fields of probability theory and mathematical physics. The material is accessible to anyone who has attended a graduate course in probability.
Author : Fereydoon Family
Publisher : World Scientific
ISBN 13 : 9789810207205
Total Pages : 500 pages
Book Rating : 4.2/5 (72 download)
Download or read book Dynamics of Fractal Surfaces written by Fereydoon Family and published by World Scientific. This book was released on 1991 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few years there has been an explosion of activity in the field of the dynamics of fractal surfaces, which, through the convergence of important new results from computer simulations, analytical theories and experiments, has led to significant advances in our understanding of nonequilibrium surface growth phenomena. This interest in surface growth phenomena has been motivated largely by the fact that a wide variety of natural and industrial processes lead to the formation of rough surfaces and interfaces. This book presents these developments in a single volume by bringing together the works containing the most important results in the field.The material is divided into chapters consisting of reprints related to a single major topic. Each chapter has a general introduction to a particular aspect of growing fractal surfaces. These introductory parts are included in order to provide a scientific background to the papers reproduced in the main part of the chapters. They are written in a pedagogical style and contain only the most essential information. The contents of the reprints are made more accessible to the reader as they are preceded by a short description of what the editors find to be the most significant results in the paper.
Author :
Publisher :
ISBN 13 :
Total Pages : 1422 pages
Book Rating : 4.3/5 (97 download)
Download or read book Physical Review written by and published by . This book was released on 2000-10 with total page 1422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.
Author : Alan McKane
Publisher : Springer Science & Business Media
ISBN 13 : 1489914218
Total Pages : 344 pages
Book Rating : 4.4/5 (899 download)
Download or read book Scale Invariance, Interfaces, and Non-Equilibrium Dynamics written by Alan McKane and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on "Scale Invariance, Interfaces and Non Equilibrium Dynamics" was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK from 20-30 June 1994. The topics discussed at the Institute were all concerned with the origin and nature of complex structures found far from equilibrium. Examples ranged from reaction diffusion systems and hydrodynamics through to surface growth due to deposition. A common theme was that of scale invariance due to the self-similarity of the underly ing structures. The topics that were covered can be broadly classified as pattern for mation (theoretical, computational and experimental aspects), the non-equilibrium dynamics of the growth of interfaces and other manifolds, coarsening phenomena, generic scale invariance in driven systems and the concept of self-organized critical ity. The main feature of the Institute was the four one-hour-Iong lectures given each day by invited speakers. In addition to thirty-seven of these lectures, two contributed lectures were also given. The many questions that were asked after the lectures attested to the excitement and interest that the lecturers succeeded in generating amongst the students. In addition to the discussions initiated by lectures, an im portant component of the meeting were the poster sessions, where participants were able to present their own work, which took place on three of the afternoons. The list of titles given at the end of these proceedings gives some idea of the range and scope of these posters.
Author : Alexei Borodin
Publisher : American Mathematical Soc.
ISBN 13 : 1470452804
Total Pages : 498 pages
Book Rating : 4.4/5 (74 download)
Download or read book Random Matrices written by Alexei Borodin and published by American Mathematical Soc.. This book was released on 2019-10-30 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.
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.
