Lectures on Random Lozenge Tilings
eBook - PDF

Lectures on Random Lozenge Tilings

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Lectures on Random Lozenge Tilings

About this book

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.

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Yes, you can access Lectures on Random Lozenge Tilings by Vadim Gorin in PDF and/or ePUB format, as well as other popular books in Mathematics & Discrete Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Series information
  4. Title page
  5. Copyright information
  6. Contents
  7. Preface
  8. 1 Lecture 1: Introduction and Tileability
  9. 2 Lecture 2: Counting Tilings through Determinants
  10. 3 Lecture 3: Extensions of the Kasteleyn Theorem
  11. 4 Lecture 4: Counting Tilings on a Large Torus
  12. 5 Lecture 5: Monotonicity and Concentration for Tilings
  13. 6 Lecture 6: Slope and Free Energy
  14. 7 Lecture 7: Maximizers in the Variational Principle
  15. 8 Lecture 8: Proof of the Variational Principle
  16. 9 Lecture 9: Euler–Lagrange and Burgers Equations
  17. 10 Lecture 10: Explicit Formulas for Limit Shapes
  18. 11 Lecture 11: Global Gaussian Fluctuations for the Heights
  19. 12 Lecture 12: Heuristics for the Kenyon–Okounkov Conjecture
  20. 13 Lecture 13: Ergodic Gibbs Translation-Invariant Measures
  21. 14 Lecture 14: Inverse Kasteleyn Matrix for Trapezoids
  22. 15 Lecture 15: Steepest Descent Method for Asymptotic Analysis
  23. 16 Lecture 16: Bulk Local Limits for Tilings of Hexagons
  24. 17 Lecture 17: Bulk Local Limits Near Straight Boundaries
  25. 18 Lecture 18: Edge Limits of Tilings of Hexagons
  26. 19 Lecture 19: The Airy Line Ensemble and Other Edge Limits
  27. 20 Lecture 20: GUE-Corners Process and Its Discrete Analogues
  28. 21 Lecture 21: Discrete Log-Gases
  29. 22 Lecture 22: Plane Partitions and Schur Functions
  30. 23 Lecture 23: Limit Shape and Fluctuations for Plane Partitions
  31. 24 Lecture 24: Discrete Gaussian Component in Fluctuations
  32. 25 Lecture 25: Sampling Random Tilings
  33. References
  34. Index