Lectures on Random Lozenge Tilings

Lectures on Random Lozenge Tilings

This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.

Author: Vadim Gorin

Publisher: Cambridge University Press

ISBN: 9781108843966

Category: Language Arts & Disciplines

Page: 200

View: 156

This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
Categories: Language Arts & Disciplines

Lectures on Random Lozenge Tilings

Lectures on Random Lozenge Tilings

For uniformly random lozenge tilings, the liquid and frozen phases exhaust the list ... of Lecture 1) at a single point (x, y) – the weight of the tiling is ...

Author: Vadim Gorin

Publisher: Cambridge University Press

ISBN: 9781108922906

Category: Mathematics

Page:

View: 172

Over the past 25 years, there has been an explosion of interest in the area of random tilings. The first book devoted to the topic, this timely text describes the mathematical theory of tilings. It starts from the most basic questions (which planar domains are tileable?), before discussing advanced topics about the local structure of very large random tessellations. The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field. The book is based on upper-division courses taught to a variety of students but it also serves as a self-contained introduction to the subject. Test your understanding with the exercises provided and discover connections to a wide variety of research areas in mathematics, theoretical physics, and computer science, such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems.
Categories: Mathematics

Lectures on Random Interfaces

Lectures on Random Interfaces

The limit shape and fluctuations of random partitions of naturals with fixed number of summands. ... of lozenge tiling and card shuffling Markov chains.

Author: Tadahisa Funaki

Publisher: Springer

ISBN: 9789811008498

Category: Mathematics

Page: 138

View: 579

Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book.Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers.Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit.A sharp interface limit for the Allen–Cahn equation, that is, a reaction–diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg–Landau model, stochastic quantization, or dynamic P(φ)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed.The Kardar–Parisi–Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied.
Categories: Mathematics

Exact Methods in Low dimensional Statistical Physics and Quantum Computing

Exact Methods in Low dimensional Statistical Physics and Quantum Computing

Lecture Notes of the Les Houches Summer School: Volume 89, ... 12.2.2 Random tilings e455 Look at the larger domino picture and lozenge picture in Figs.

Author: Jesper Jacobsen

Publisher: OUP Oxford

ISBN: 9780191574443

Category: Science

Page: 664

View: 517

Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics.
Categories: Science

Thirty three Miniatures

Thirty three Miniatures

It can be ob- tained, with some effort, as lecture notes of the University ... for permission to use his picture of a random lozenge tiling in Miniature 22, ...

Author:

Publisher: American Mathematical Soc.

ISBN: 9780821849774

Category:

Page:

View: 759

Categories:

Markov Chains and Mixing Times Second Edition

Markov Chains and Mixing Times  Second Edition

A lower bound for the mixing time of the random-to-random insertions shuffle, Electron. ... Mixing times of lozenge tiling and card shuffling Markov chains, ...

Author: David A. Levin

Publisher: American Mathematical Soc.

ISBN: 9781470429621

Category: Distribution (Probability theory)

Page: 447

View: 911

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.
Categories: Distribution (Probability theory)

LATIN 98 Theoretical Informatics

LATIN 98  Theoretical Informatics

Random Structures and Algorithms 7 , 1995 , pp . 157-165 . ... Wilson , D.B. Mixing times of lozenge tiling and card shuffling Markov chains , The CREW PRAM ...

Author: Claudio L. Lucchesi

Publisher: Springer Science & Business Media

ISBN: 3540642757

Category: Computers

Page: 390

View: 816

This book constitutes the refereed proceedings of the Third Latin American Symposium on Theoretical Informatics, LATIN'98, held in Campinas, Brazil, in April 1998. The 28 revised full papers presented together with five invited surveys were carefully selected from a total of 53 submissions based on 160 referees' reports. The papers are organized in sections on algorithms and complexity; automata, transition systems and combinatorics on words; computational geometry and graph drawing; cryptography; graph theory and algorithms on graphs; packet routing; parallel algorithms; and pattern matching and browsing.
Categories: Computers

Groups St Andrews 2001 in Oxford Volume 1

Groups St Andrews 2001 in Oxford  Volume 1

Lectures on finite Markov Chains , Lecture Notes in Math . 1665 , Springer , Berlin . ... Mixing times of Lozenge tiling and card shuffling Markov Chains .

Author: C. M. Campbell

Publisher: Cambridge University Press

ISBN: 1139437216

Category: Mathematics

Page:

View: 988

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.
Categories: Mathematics

Randomization Methods in Algorithm Design

Randomization Methods in Algorithm Design

[ 2 ] P. Diaconis and L. Saloff - Coste , Comparison technique for random ... Mixing times of lozenge tiling and card shuffling Markov chains , draft of ...

Author: Panos M. Pardalos

Publisher: American Mathematical Soc.

ISBN: 0821870874

Category: Mathematics

Page: 318

View: 414

Categories: Mathematics

New Perspectives in Algebraic Combinatorics

New Perspectives in Algebraic Combinatorics

... number of centered lozenge tilings of a symmetric hexagon ” , J. Combin . ... statistics for random domino tilings of the Aztec diamond ” , Duke Math .

Author: Louis J. Billera

Publisher: Cambridge University Press

ISBN: 0521770874

Category: Mathematics

Page: 345

View: 390

This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.
Categories: Mathematics

Proceedings of the Ninth Annual ACM SIAM Symposium on Discrete Algorithms

Proceedings of the Ninth Annual ACM SIAM Symposium on Discrete Algorithms

[ 10 ] M. Dyer , A. Frieze , and R. Kannan , A random polynomial - time ... times of lozenge tiling and card www.berkeley.edu/users/aldous/book.html .

Author: Howard Karloff

Publisher: SIAM

ISBN: 0898714109

Category: Algorithms

Page: 704

View: 325

This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.
Categories: Algorithms

Randomized Algorithms Approximation Generation and Counting

Randomized Algorithms  Approximation  Generation  and Counting

Mixing times of lozenge tiling and card shuffling Markov chains, August 1997. ... Annotated bibliography of perfectly random sampling with Markov chains.

Author: Russ Bubley

Publisher: Springer Science & Business Media

ISBN: 9781447106951

Category: Computers

Page: 152

View: 679

Randomized Algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability. When asking questions like "How many are there?" and "What does it look like on average?" of families of combinatorial structures, answers are often difficult to find -- we can be blocked by seemingly intractable algorithms. Randomized Algorithms shows how to get around the problem of intractability with the Markov chain Monte Carlo method, as well as highlighting the method's natural limits. It uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.
Categories: Computers

LATIN 2010 Theoretical Informatics

LATIN 2010  Theoretical Informatics

Academic Press, New York (1968) [TV01] Tetali, P., Vempala, S.: Random sampling ... D.B.: Mixing times of Lozenge tiling and card shuffling Markov chains.

Author: Alejandro López-Ortiz

Publisher: Springer Science & Business Media

ISBN: 9783642121999

Category: Computers

Page: 706

View: 345

This book constitutes the refereed proceedings of the 9th International Latin American Symposium on Theoretical Informatics, LATIN 2010, held in Oaxaca, Mexico; in April 2010. The 56 revised full papers presented together with the abstracts of 4 invited plenary talks were carefully reviewed and selected from 155 submissions. The papers address a variety of topics in theoretical computer science with a certain focus on algorithms, automata theory and formal languages, coding theory and data compression, algorithmic graph theory and combinatorics, complexity theory, computational algebra, computational biology, computational geometry, computational number theory, cryptography, theoretical aspects of databases and information retrieval, data structures, networks, logic in computer science, machine learning, mathematical programming, parallel and distributed computing, pattern matching, quantum computing and random structures.
Categories: Computers

Estimated Mixing Times

Estimated Mixing Times

( SC96 ] Laurent Saloff - Coste , Lectures on finite markov chains ... ( Wil04 ] > Mixing times of lozenge tiling and card shuffling markov chains ...

Author: Sharad Chandra Goel

Publisher:

ISBN: CORNELL:31924103605519

Category:

Page: 256

View: 982

Categories:

FOCS 2004

FOCS 2004

Before the mixing time of the cyclicto - random shuffle , ' traces " of the ... of lozenge tiling and card shuffling Markov chains , Ann . Applied Probab .

Author:

Publisher: Institute of Electrical & Electronics Engineers(IEEE)

ISBN: 0769522289

Category: Computational complexity

Page: 632

View: 469

Annotation The proceedings covers computational complexity, cryptography, parallel and distributed computing, machine learning, logic, coding theory, theoretical databases, information technology, networks, quantum computing, and much more.
Categories: Computational complexity

Probability and Statistical Physics in St Petersburg

Probability and Statistical Physics in St  Petersburg

A computer simulation showing the connection with tilings can be found on ... t can be identified with a lozenge tiling of a sector in the plane and with a ...

Author: V. Sidoravicius

Publisher: American Mathematical Soc.

ISBN: 9781470422486

Category: Combinatorial analysis

Page: 471

View: 563

This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Categories: Combinatorial analysis

STACS 2007

STACS 2007

Random Structures and Algorithm, I(4):447–460, 1990. 15. L. Gasieniec and A. Pelc. ... Mixing times of lozenge tiling and card shuffling markov chains.

Author: Wolfgang Thomas

Publisher: Springer Science & Business Media

ISBN: 9783540709176

Category: Computers

Page: 708

View: 117

This book constitutes the refereed proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007, held in Aachen, Germany in February 2007. The 56 revised full papers presented together with 3 invited papers were carefully reviewed and selected from about 400 submissions. The papers address the whole range of theoretical computer science including algorithms and data structures, automata and formal languages, complexity theory, logic in computer science, semantics, specification, and verification of programs, rewriting and deduction, as well as current challenges like biological computing, quantum computing, and mobile and net computing.
Categories: Computers

Mathematical Reviews

Mathematical Reviews

( English summary ) Igorith theory - SWAT 2002 , 160–169 , Lecture Notes in ... Mihai ) Enumeration of Lozenge tilings of hexagons with cut - off corners .

Author:

Publisher:

ISBN: UVA:X006180726

Category: Mathematics

Page:

View: 860

Categories: Mathematics

Resenhas IME USP

Resenhas IME USP

123 of London Mathematical Lecture Notes , Cambridge University Press ... Mickiewicz UniAn Overview of Domino and Lozenge Tilings Nicolau C. Saldanha and.

Author:

Publisher:

ISBN: UOM:39015049323713

Category: Mathematics

Page:

View: 162

Categories: Mathematics