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Author : Guan-Yu Chen
Publisher :
ISBN 13 :
Total Pages : 478 pages
Book Rating : 4.E/5 ( download)
Download or read book The Cutoff Phenomenon for Finite Markov Chains written by Guan-Yu Chen and published by . This book was released on 2006 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.1/5 (85 download)
Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Author : Avrim Blum
Publisher : Cambridge University Press
ISBN 13 : 1108617360
Total Pages : 433 pages
Book Rating : 4.1/5 (86 download)
Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.
Author : David A. Levin
Publisher : American Mathematical Soc.
ISBN 13 : 1470429624
Total Pages : 465 pages
Book Rating : 4.4/5 (74 download)
Download or read book Markov Chains and Mixing Times written by David A. Levin and published by American Mathematical Soc.. This book was released on 2017-10-31 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.
Author : Vlastimil Dlab
Publisher : American Mathematical Soc.
ISBN 13 : 0821834169
Total Pages : 502 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on 2004 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ``instructional'' workshop preceding the conference, there were also workshops on ``Commutative Algebra, Algebraic Geometry and Representation Theory'', ``Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ``Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Author : J. Keilson
Publisher : Springer Science & Business Media
ISBN 13 : 1461262003
Total Pages : 199 pages
Book Rating : 4.4/5 (612 download)
Download or read book Markov Chain Models — Rarity and Exponentiality written by J. Keilson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: in failure time distributions for systems modeled by finite chains. This introductory chapter attempts to provide an over view of the material and ideas covered. The presentation is loose and fragmentary, and should be read lightly initially. Subsequent perusal from time to time may help tie the mat erial together and provide a unity less readily obtainable otherwise. The detailed presentation begins in Chapter 1, and some readers may prefer to begin there directly. §O.l. Time-Reversibility and Spectral Representation. Continuous time chains may be discussed in terms of discrete time chains by a uniformizing procedure (§2.l) that simplifies and unifies the theory and enables results for discrete and continuous time to be discussed simultaneously. Thus if N(t) is any finite Markov chain in continuous time governed by transition rates vmn one may write for pet) = [Pmn(t)] • P[N(t) = n I N(O) = m] pet) = exp [-vt(I - a )] (0.1.1) v where v > Max r v ' and mn m n law ~ 1 - v-I * Hence N(t) where is governed r vmn Nk = NK(t) n K(t) is a Poisson process of rate v indep- by a ' and v dent of N • k Time-reversibility (§1.3, §2.4, §2.S) is important for many reasons. A) The only broad class of tractable chains suitable for stochastic models is the time-reversible class.
Author : Harry Kesten
Publisher : Springer
ISBN 13 : 9783662094457
Total Pages : 351 pages
Book Rating : 4.0/5 (944 download)
Download or read book Probability on Discrete Structures written by Harry Kesten and published by Springer. This book was released on 2012-12-22 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
Author : Diaraf Seck
Publisher : Springer Nature
ISBN 13 : 3030573362
Total Pages : 462 pages
Book Rating : 4.0/5 (35 download)
Download or read book Nonlinear Analysis, Geometry and Applications written by Diaraf Seck and published by Springer Nature. This book was released on 2020-11-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.
Author : Ravi R. Montenegro
Publisher : Now Publishers Inc
ISBN 13 : 1933019298
Total Pages : 133 pages
Book Rating : 4.9/5 (33 download)
Download or read book Mathematical Aspects of Mixing Times in Markov Chains written by Ravi R. Montenegro and published by Now Publishers Inc. This book was released on 2006 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Aspects of Mixing Times in Markov Chains is a comprehensive, well-written review of the subject that will be of interest to researchers and students in computer and mathematical sciences.
Author : D N Shanbhag
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444500144
Total Pages : 990 pages
Book Rating : 4.5/5 (1 download)
Download or read book Stochastic Processes: Theory and Methods written by D N Shanbhag and published by Gulf Professional Publishing. This book was released on 2001 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.
Author : Peter G. Doyle
Publisher : American Mathematical Soc.
ISBN 13 : 1614440220
Total Pages : 174 pages
Book Rating : 4.6/5 (144 download)
Download or read book Random Walks and Electric Networks written by Peter G. Doyle and published by American Mathematical Soc.. This book was released on 1984-12-31 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
Author : Evarist Giné
Publisher : Springer
ISBN 13 : 354069210X
Total Pages : 431 pages
Book Rating : 4.5/5 (46 download)
Download or read book Lectures on Probability Theory and Statistics written by Evarist Giné and published by Springer. This book was released on 2006-11-14 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nur Contents aufnehmen
Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
ISBN 13 : 9780521883368
Total Pages : 454 pages
Book Rating : 4.8/5 (833 download)
Download or read book Harmonic Analysis on Finite Groups written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2008-03-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space, this book develops the necessary tools for the asymptotic analysis of these processes. Its topics range from the basic theory needed for students new to this area, to advanced topics such as the theory of Green's algebras, the complete analysis of the random matchings, and a presentation of the presentation theory of the symmetric group. This self-contained, detailed study culminates with case-by-case analyses of the cut-off phenomenon discovered by Persi Diaconis.
Author : E. Goles
Publisher : Springer Science & Business Media
ISBN 13 : 9401009201
Total Pages : 306 pages
Book Rating : 4.4/5 (1 download)
Download or read book Complex Systems written by E. Goles and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the courses given at the Sixth Summer School on Complex Systems held at Facultad de Ciencias Fisicas y Maternaticas, Universidad de Chile at Santiago, Chile, from 14th to 18th December 1998. This school was addressed to graduate students and researchers working on areas related with recent trends in Complex Systems, including dynamical systems, cellular automata, complexity and cutoff in Markov chains. Each contribution is devoted to one of these subjects. In some cases they are structured as surveys, presenting at the same time an original point of view and showing mostly new results. The paper of Pierre Arnoux investigates the relation between low complex systems and chaotic systems, showing that they can be put into relation by some re normalization operations. The case of quasi-crystals is fully studied, in particular the Sturmian quasi-crystals. The paper of Franco Bagnoli and Raul Rechtman establishes relations be tween Lyapunov exponents and synchronization processes in cellular automata. The principal goal is to associate tools, usually used in physical problems, to an important problem in cellularautomata and computer science, the synchronization problem. The paper of Jacques Demongeot and colleagues gives a presentation of at tractors of dynamical systems appearing in biological situations. For instance, the relation between positive or negative loops and regulation systems.
Author : C. M. Campbell
Publisher : Cambridge University Press
ISBN 13 : 9781139437219
Total Pages : 316 pages
Book Rating : 4.4/5 (372 download)
Download or read book Groups St Andrews 2001 in Oxford: Volume 1 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2003-11-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past twenty years. As with earlier volumes, these refereed volumes also contain accessible surveys of contemporary research fronts, as well as a diverse collection of short research articles. They form a valuable reference for researchers, especially graduate students, working in group theory.
Author : Audrey Terras
Publisher : Cambridge University Press
ISBN 13 : 9780521457187
Total Pages : 456 pages
Book Rating : 4.4/5 (571 download)
Download or read book Fourier Analysis on Finite Groups and Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 1999-03-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Author : John G Kemeny
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (513 download)
Download or read book Finite Markov Chains written by John G Kemeny and published by . This book was released on 1960 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
