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  3. Lectures on Random Lozenge Tilings
  • Cited by 23
Publisher:
Cambridge University Press
Online publication date:
August 2021
Print publication year:
2021
Online ISBN:
9781108921183
DOI:
https://doi.org/10.1017/9781108921183
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Studies in Advanced Mathematics (193)
Information

Book description

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.

Reviews

‘The lectures provide connections between random tilings and many areas in mathematics and theoretical physics, and include an exhaustive reference list. Mathematicians and others interested in the hows and whys of this intriguing area would be well-served by consulting this text.’

Thomas Polaski Source: Mathematical Reviews/MathSciNet

‘It seems that the reviewed book is the first introductory text about this fascinating topic. The release of this book is a great event for everyone interested in this problem.’

Anton Shutov Source: zbMATH

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