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Universality For Some Random Growth Models
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Book Synopsis Universality for Some Random Growth Models by : Kevin Yang
Download or read book Universality for Some Random Growth Models written by Kevin Yang and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies the problem of deriving fluctuations of hydrodynamic limits for general time-dependent microscopic systems. To this end, we develop a derivation of the Boltzmann-Gibbs principle depending only on the dynamics of the system at hand. This provides an answer to conjectures of Spohn and Jensen-Yau. As an application of the method, we derive the Kardar-Parisi-Zhang equation as a continuum limit of the current fluctuations in some non-integrable and non-stationary asymmetric exclusion processes.
Book Synopsis Random Growth Models by : Michael Damron
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 274 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.
Book Synopsis Universality of Some Models of Random Matrices and Random Processes by : Alexey Naumov
Download or read book Universality of Some Models of Random Matrices and Random Processes written by Alexey Naumov and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reflected Brownian Motions in the KPZ Universality Class by : Thomas Weiss
Download or read book Reflected Brownian Motions in the KPZ Universality Class written by Thomas Weiss and published by Springer. This book was released on 2016-12-16 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.
Book Synopsis Scaling and Universality in Deposition Models of Growth by :
Download or read book Scaling and Universality in Deposition Models of Growth written by and published by . This book was released on 2010 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Dynamical Approach to Random Matrix Theory by : László Erdős
Download or read book A Dynamical Approach to Random Matrix Theory written by László Erdős and published by American Mathematical Soc.. This book was released on 2017-08-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Book Synopsis Random Fluctuations and Pattern Growth: Experiments and Models by : Harry Eugene Stanley
Download or read book Random Fluctuations and Pattern Growth: Experiments and Models written by Harry Eugene Stanley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Cargèse, Corsica, France, 18-31 July, 1988
Book Synopsis Brownian Regularity for the Airy Line Ensemble, and Multi-Polymer Watermelons in Brownian Last Passage Percolation by : Alan Hammond
Download or read book Brownian Regularity for the Airy Line Ensemble, and Multi-Polymer Watermelons in Brownian Last Passage Percolation written by Alan Hammond and published by American Mathematical Society. This book was released on 2022-05-24 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Universality In Nonequilibrium Lattice Systems: Theoretical Foundations by : Geza Odor
Download or read book Universality In Nonequilibrium Lattice Systems: Theoretical Foundations written by Geza Odor and published by World Scientific. This book was released on 2008-05-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. Based on a review in Rev. Mod. Phys. by the author, it incorporates surface growth classes, classes of spin models, percolation and multi-component system classes as well as damage spreading transitions. (The success of that review can be quantified by the more than one hundred independent citations of that paper since 2004.)The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results. Topological phase space diagrams introduced by Kamenev (Physical Review E 2006) very recently are used as a guide for one-component, reaction-diffusion systems.
Book Synopsis Topics in Random Growth Models by : Finn, Thomas
Download or read book Topics in Random Growth Models written by Finn, Thomas and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integrable Systems and Random Matrices by : Jinho Baik
Download or read book Integrable Systems and Random Matrices written by Jinho Baik and published by American Mathematical Soc.. This book was released on 2008 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.
Book Synopsis Physical Properties of Polymers Handbook by : James E. Mark
Download or read book Physical Properties of Polymers Handbook written by James E. Mark and published by Springer Science & Business Media. This book was released on 2007-03-21 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers concise information on the properties of polymeric materials, particularly those most relevant to physical chemistry and chemical physics. Extensive updates and revisions to each chapter include eleven new chapters on novel polymeric structures, reinforcing phases in polymers, and experiments on single polymer chains. The study of complex materials is highly interdisciplinary, and new findings are scattered among a large selection of scientific and engineering journals. This book brings together data from experts in the different disciplines contributing to the rapidly growing area of polymers and complex materials.
Book Synopsis Fractals, Scaling and Growth Far from Equilibrium by : Paul Meakin
Download or read book Fractals, Scaling and Growth Far from Equilibrium written by Paul Meakin and published by Cambridge University Press. This book was released on 1998 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.
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.
Book Synopsis Leveraging Distortions by : Collin Rice
Download or read book Leveraging Distortions written by Collin Rice and published by MIT Press. This book was released on 2021-08-17 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: An examination of how scientists deliberately and justifiably use pervasive distortions of relevant features to explain and understand natural phenomena. A fundamental rule of logic is that in order for an argument to provide good reasons for its conclusion, the premises of the argument must be true. In this book, Collin Rice shows how the practice of science repeatedly, pervasively, and deliberately violates this principle. Rice argues that scientists strategically use distortions that misrepresent relevant features of natural phenomena in order to explain and understand--and that they use these distortions deliberately and justifiably in order to discover truths that would be otherwise inaccessible. Countering the standard emphasis on causation, accurate representation, and decomposition of science into its accurate and inaccurate parts, Rice shows that science's epistemic achievements can still be factive despite their being produced through the use of holistically distorted scientific representations. Indeed, he argues, this distortion is one of the most widely employed and fruitful tools used in scientific theorizing. Marshalling a range of case studies, Rice contends that many explanations in science are noncausal, and he presents an alternate view of explanation that captures the variety of noncausal explanations found across the sciences. He proposes an alternative holistic distortion view of idealized models, connecting it to physicists' concept of a universality class; shows how universality classes can overcome some of the challenges of multiscale modeling; and offers accounts of explanation, idealization, modeling, and understanding.
Author : Publisher :World Scientific ISBN 13 : Total Pages :1131 pages Book Rating :4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1131 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Aspects of Functional Analysis by : Vitali D. Milman
Download or read book Geometric Aspects of Functional Analysis written by Vitali D. Milman and published by Springer. This book was released on 2007-04-27 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 reflects the general trends of the theory and are a source of inspiration for research. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies to the study of sections or projections of convex bodies.
