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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 : 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 : 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 : 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 : 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 :
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 : 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 : 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 :
Publisher :
ISBN 13 :
Total Pages : 1162 pages
Book Rating : 4.3/5 (91 download)
Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 1162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vadim Gorin
Publisher : Cambridge University Press
ISBN 13 : 1108843964
Total Pages : 261 pages
Book Rating : 4.1/5 (88 download)
Download or read book Lectures on Random Lozenge Tilings written by Vadim Gorin and published by Cambridge University Press. This book was released on 2021-09-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
Author : Milton Abramowitz
Publisher :
ISBN 13 :
Total Pages : 476 pages
Book Rating : 4.F/5 ( download)
Download or read book Pocketbook of Mathematical Functions written by Milton Abramowitz and published by . This book was released on 1984 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John J. Kasianowicz
Publisher : Springer Science & Business Media
ISBN 13 : 9781402006975
Total Pages : 46 pages
Book Rating : 4.0/5 (69 download)
Download or read book Structure and Dynamics of Confined Polymers written by John J. Kasianowicz and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymers are essential to biology because they can have enough stable degrees of freedom to store the molecular code of heredity and to express the sequences needed to manufacture new molecules. Through these they perform or control virtually every function in life. Although some biopolymers are created and spend their entire career in the relatively large free space inside cells or organelles, many biopolymers must migrate through a narrow passageway to get to their targeted destination. This suggests the questions: How does confining a polymer affect its behavior and function? What does that tell us about the interactions between the monomers that comprise the polymer and the molecules that confine it? Can we design and build devices that mimic the functions of these nanoscale systems? The NATO Advanced Research Workshop brought together for four days in Bikal, Hungary over forty experts in experimental and theoretical biophysics, molecular biology, biophysical chemistry, and biochemistry interested in these questions. Their papers collected in this book provide insight on biological processes involving confinement and form a basis for new biotechnological applications using polymers. In his paper Edmund DiMarzio asks: What is so special about polymers? Why are polymers so prevalent in living things? The chemist says the reason is that a protein made of N amino acids can have any of 20 different kinds at each position along the chain, resulting in 20 N different polymers, and that the complexity of life lies in this variety.
Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 3540328912
Total Pages : 392 pages
Book Rating : 4.5/5 (43 download)
Download or read book The Random-Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
