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Author : Manuela Girotti
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Riemann-Hilbert Approach to Gap Probabilities of Determinantal Point Processes written by Manuela Girotti and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Galina Filipuk
Publisher : American Mathematical Society
ISBN 13 : 147046604X
Total Pages : 240 pages
Book Rating : 4.4/5 (74 download)
Download or read book Recent Trends in Formal and Analytic Solutions of Diff. Equations written by Galina Filipuk and published by American Mathematical Society. This book was released on 2023-02-09 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Formal and Analytic Solutions of Diff. Equations, held from June 28–July 2, 2021, and hosted by University of Alcalá, Alcalá de Henares, Spain. The manuscripts cover recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, moment differential equations, etc. Also discussed are related topics such as summability of formal solutions and the asymptotic study of their solutions. The volume is intended not only for researchers in this field of knowledge but also for students who aim to acquire new techniques and learn recent results.
Author : John Harnad
Publisher : Springer Science & Business Media
ISBN 13 : 1441995145
Total Pages : 536 pages
Book Rating : 4.4/5 (419 download)
Download or read book Random Matrices, Random Processes and Integrable Systems written by John Harnad and published by Springer Science & Business Media. This book was released on 2011-05-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.
Author : Greg W. Anderson
Publisher : Cambridge University Press
ISBN 13 : 0521194520
Total Pages : 507 pages
Book Rating : 4.5/5 (211 download)
Download or read book An Introduction to Random Matrices written by Greg W. Anderson and published by Cambridge University Press. This book was released on 2010 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Author : László Erdős
Publisher : American Mathematical Soc.
ISBN 13 : 1470436485
Total Pages : 239 pages
Book Rating : 4.4/5 (74 download)
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.
Author : Pavel Bleher
Publisher : American Mathematical Soc.
ISBN 13 : 1470409615
Total Pages : 237 pages
Book Rating : 4.4/5 (74 download)
Download or read book Random Matrices and the Six-Vertex Model written by Pavel Bleher and published by American Mathematical Soc.. This book was released on 2013-12-04 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed description of the Riemann-Hilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the six-vertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric. Titles in this series are co-published with the Centre de Recherches Mathématiques.
Author : Percy Deift
Publisher : American Mathematical Soc.
ISBN 13 : 0821826956
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)
Download or read book Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach written by Percy Deift and published by American Mathematical Soc.. This book was released on 2000 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Author : D. V. Anosov
Publisher : Springer Science & Business Media
ISBN 13 : 3322929094
Total Pages : 202 pages
Book Rating : 4.3/5 (229 download)
Download or read book The Riemann-Hilbert Problem written by D. V. Anosov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.
Author : Günter Last
Publisher : Cambridge University Press
ISBN 13 : 1107088011
Total Pages : 315 pages
Book Rating : 4.1/5 (7 download)
Download or read book Lectures on the Poisson Process written by Günter Last and published by Cambridge University Press. This book was released on 2017-10-26 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
ISBN 13 : 1108317995
Total Pages : 225 pages
Book Rating : 4.1/5 (83 download)
Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 0821874306
Total Pages : 298 pages
Book Rating : 4.8/5 (218 download)
Download or read book Topics in Random Matrix Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2012-03-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)
Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author : Motoko Kotani
Publisher : Advanced Studies in Pure Mathe
ISBN 13 : 9784931469587
Total Pages : 514 pages
Book Rating : 4.4/5 (695 download)
Download or read book Probabilistic Approach to Geometry written by Motoko Kotani and published by Advanced Studies in Pure Mathe. This book was released on 2010-03 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first Seasonal Institute of the Mathematical Society of Japan (MSJ-SI) “Probabilistic Approach to Geometry” was held at Kyoto University, Japan, on 28th July 2008 - 8th August, 2008. The conference aimed to make interactions between Geometry and Probability Theory and seek for new directions of those research areas. This volume contains the proceedings, selected research articles based on the talks, including survey articles on random groups, rough paths, and heat kernels by the survey lecturers in the conference. The readers will benefit of exploring in this developing research area.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
Author : J. Baik
Publisher : Princeton University Press
ISBN 13 : 0691127344
Total Pages : 178 pages
Book Rating : 4.6/5 (911 download)
Download or read book Discrete Orthogonal Polynomials. (AM-164) written by J. Baik and published by Princeton University Press. This book was released on 2007 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description
Author : Alice Guionnet
Publisher : Springer Science & Business Media
ISBN 13 : 3540698965
Total Pages : 296 pages
Book Rating : 4.5/5 (46 download)
Download or read book Large random matrices written by Alice Guionnet and published by Springer Science & Business Media. This book was released on 2009-03-25 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.
Author : Alex Kulesza
Publisher : Now Pub
ISBN 13 : 9781601986283
Total Pages : 178 pages
Book Rating : 4.9/5 (862 download)
Download or read book Determinantal Point Processes for Machine Learning written by Alex Kulesza and published by Now Pub. This book was released on 2012-11-29 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensible introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community.
Author : Leonid Andreevich Pastur
Publisher : American Mathematical Soc.
ISBN 13 : 082185285X
Total Pages : 650 pages
Book Rating : 4.8/5 (218 download)
Download or read book Eigenvalue Distribution of Large Random Matrices written by Leonid Andreevich Pastur and published by American Mathematical Soc.. This book was released on 2011 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
