Markov Chains and Mixing Times

Author: David Asher Levin,Yuval Peres,Elizabeth Lee Wilmer

Publisher: American Mathematical Soc.

ISBN: 9780821886274

Category: Mathematics

Page: 371

View: 2437

This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of random walks on networks, including hitting and cover times, and analyses of several methods of shuffling cards. As a prerequisite, the authors assume a modest understanding of probability theory and linear algebra at an undergraduate level. Markov Chains and Mixing Times is meant to bring the excitement of this active area of research to a wide audience.

Markov Chains and Mixing Times: Second Edition

Author: David A. Levin,Yuval Peres

Publisher: American Mathematical Soc.

ISBN: 1470429624

Category: Distribution (Probability theory)

Page: 447

View: 6500

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.

Die Statistik

zwölf Stationen des statistischen Arbeitens

Author: Günter Menges

Publisher: N.A

ISBN: N.A

Category: Statistics

Page: 505

View: 7285


Approximative Algorithmen und Nichtapproximierbarkeit

Author: Klaus Jansen,Marian Margraf

Publisher: Walter de Gruyter

ISBN: 3110203170

Category: Mathematics

Page: 501

View: 7629

Gegenstand dieses Lehrbuchs ist die Behandlung schwer lösbarer diskreter Optimierungsprobleme. Im ersten Teil werden schnelle Algorithmen vorgestellt, die solche Probleme näherungsweise lösen können. Der zweite Teil behandelt Komplexitätstheorie und Nichtapproximierbarkeit von Optimierungsproblemen. Das Lehrbuch enthält zudem zahlreiche Anwendungsbeispiele, Übungsaufgaben, Illustrationen und Abschnitte über Grundlagen wie etwa die Turingmaschine.

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662577674

Category: Mathematics

Page: 360

View: 2232

Diese fünfte deutsche Auflage enthält ein ganz neues Kapitel über van der Waerdens Permanenten-Vermutung, sowie weitere neue, originelle und elegante Beweise in anderen Kapiteln. Aus den Rezensionen: “... es ist fast unmöglich, ein Mathematikbuch zu schreiben, das von jedermann gelesen und genossen werden kann, aber Aigner und Ziegler gelingt diese Meisterleistung in virtuosem Stil. [...] Dieses Buch erweist der Mathematik einen unschätzbaren Dienst, indem es Nicht-Mathematikern vorführt, was Mathematiker meinen, wenn sie über Schönheit sprechen.” Aus der Laudatio für den “Steele Prize for Mathematical Exposition” 2018 "Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdös immer wieder zitierte BUCH gehören, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Sätze enthält. Manchmal lässt der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, überraschenden Zusammenhängen und unerwarteten Volten." www.mathematik.de, Mai 2002 "Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdös, verständlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Lösungen mit Aha-Effekt, auch für Nicht-Mathematiker." www.vismath.de "Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999 "Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern." www.mathematik.de, Mai 2002

Kalman-Bucy-Filter

Deterministische Beobachtung und stochastische Filterung

Author: Karl Brammer,Gerhard Siffling

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486785524

Category: Science

Page: 232

View: 5547

Das Buch führt den Leser auf elementarem Wege in die Wahrscheinlichkeitsrechnung und in die Theorie der Zufallsprozesse ein, wobei keinerlei Vorkenntnisse auf diesem Gebiet vorausgesetzt werden. Schließlich wird gezeigt, wie sich die Eigenschaften eines Zufallsprozesses bei der Übertragung durch ein lineares System verändern und wie diese veränderten Eigenschaften berechnet werden können.

Introduction to Markov Chains

With Special Emphasis on Rapid Mixing

Author: Ehrhard Behrends

Publisher: Vieweg+Teubner Verlag

ISBN: 3322901572

Category: Mathematics

Page: 234

View: 6952

Besides the investigation of general chains the book contains chapters which are concerned with eigenvalue techniques, conductance, stopping times, the strong Markov property, couplings, strong uniform times, Markov chains on arbitrary finite groups (including a crash-course in harmonic analysis), random generation and counting, Markov random fields, Gibbs fields, the Metropolis sampler, and simulated annealing. With 170 exercises.

LATIN 2004: Theoretical Informatics

6th Latin American Symposium, Buenos Aires, Argentina, April 5-8, 2004, Proceedings

Author: Martin Farach-Colton

Publisher: Springer Science & Business Media

ISBN: 3540212582

Category: Computers

Page: 632

View: 5575

This volume contains the proceedings of the Latin American Theoretical Inf- matics (LATIN) conference that was held in Buenos Aires, Argentina, April 5–8, 2004. The LATIN series of symposia was launched in 1992 to foster interactions between the Latin American community and computer scientists around the world. This was the sixth event in the series, following S ̃ ao Paulo, Brazil (1992), Valparaiso, Chile (1995), Campinas, Brazil (1998), Punta del Este, Uruguay (2000), and Cancun, Mexico (2002). The proceedings of these conferences were also published by Springer-Verlag in the Lecture Notes in Computer Science series: Volumes 583, 911, 1380, 1776, and 2286, respectively. Also, as before, we published a selection of the papers in a special issue of a prestigious journal. We received 178 submissions. Each paper was assigned to four program c- mittee members, and 59 papers were selected. This was 80% more than the previous record for the number of submissions. We feel lucky to have been able to build on the solid foundation provided by the increasingly successful previous LATINs. And we are very grateful for the tireless work of Pablo Mart ́ ?nez L ́ opez, the Local Arrangements Chair. Finally, we thank Springer-Verlag for publishing these proceedings in its LNCS series.

Permutations with Interval Restrictions

Author: N.A

Publisher: Stanford University

ISBN: N.A

Category:

Page: N.A

View: 9787

This thesis studies the problem of the random transposition walk on permutations with interval restrictions. The mixing time of this Markov chain is explored, and a number of different cases are considered. For the case of bounded interval restrictions, a polynomial bound for the mixing time is achieved. For a specific example of bounded interval restrictions called Fibonacci permutations, the correct order of the mixing time is derived. An example of a family of interval restriction matrices for which the random walk mixes in exponential time is provided, showing that the walk in general does not mix in polynomial time. The case of one-sided interval restrictions is also studied, and cut-off is shown for a large class of one-sided interval restriction matrices. Furthermore, examples are provided in which chi-squared cut-off occurs, while total variation mixing occurs significantly earlier without cut-off. Finally, a coupling argument showing the correct order mixing time for the random transposition walk on the whole symmetric group is presented. This is achieved via projection to conjugacy classes and then a path coupling argument.

Implementation and Application of Automata

16th International Conference, CIAA 2011, Blois, France, July 13-16, 2011, Revised Selected Papers

Author: Béatrice Bouchou-Markhoff,Pascal Caron,Jean-Marc Champarnaud,Denis Maurel

Publisher: Springer

ISBN: 3642222560

Category: Computers

Page: 299

View: 6033

This book constitutes the thoroughly refereed papers of the 16th International Conference on Implementation and Application of Automata, CIAA 2011, held in Blois, France, in July 2011. The 20 revised full papers together with 4 short papers were carefully selected from 38 submissions. The papers cover various topics such as applications of automata in computer-aided verification; natural language processing; pattern matching, data storage and retrieval; document engineering and bioinformatics as well as foundational work on automata theory.

Fundamentals of Computation Theory

15th International Symposium, FCT 2005, Lübeck, Gemany, August 17-20, 2005, Proceedings

Author: Maciej Liskiewicz

Publisher: Springer Science & Business Media

ISBN: 3540281932

Category: Computers

Page: 576

View: 755

This book constitutes the refereed proceedings of the 15th International Symposium Fundamentals of Computation Theory, FCT 2005, held in Lübeck, Germany in August 2005. The 46 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on circuits, automata, complexity, approximability, computational and structural complexity, graphs and complexity, computational game theory, visual cryptography and computational geometry, query complexity, distributed systems, automata and formal languages, semantics, approximation algorithms, average case complexity, algorithms, graph algorithms, and pattern matching.