Lectures on Random Lozenge Tilings

The book "Mathematical Theory of Tilings" is a comprehensive guide to the mathematical theory of tilings, covering basic questions and advanced topics, and discussing connections to other research areas.

\n Format: Hardback
\n Length: 200 pages
\n Publication date: 09 September 2021
\n Publisher: Cambridge University Press
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Over the past quarter-century, there has been a remarkable surge of interest in the field of random tilings. This timely text serves as an invaluable resource, providing a comprehensive mathematical exposition of the subject. It begins by delving into the fundamental inquiries, such as determining which planar domains are tileable, and proceeds to explore advanced topics related to the local structure of exceedingly large random tessellations. The author elucidates each characteristic of random tilings of vast domains, presenting diverse perspectives and paving the way for open problems within the field. While the book is rooted in upper-division courses designed for a diverse student cohort, it also functions as a self-contained introduction to the topic. To reinforce understanding, the text includes a comprehensive set of exercises, enabling readers to test their knowledge and uncover connections to a wide array of research areas in mathematics, theoretical physics, and computer science. These include seminal concepts such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems. By delving into these interconnected domains, readers gain a deeper appreciation of the rich tapestry of mathematical exploration and its profound implications for understanding the world around us.

\n Weight: 526g\n
Dimension: 159 x 235 x 21 (mm)\n
ISBN-13: 9781108843966\n \n