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The scaling limit of the correlation of holes on the triangular lattice with periodic boundary conditions


About this Title

Mihai Ciucu

Publication: Memoirs of the American Mathematical Society
Publication Year 2009: Volume 199, Number 935
ISBNs: 978-0-8218-4326-0 (print); 978-1-4704-0541-0 (online)
DOI: http://dx.doi.org/10.1090/memo/0935
MathSciNet review: 2508012
MSC (2000): Primary 82B23; Secondary 05A16, 60F99, 60K35, 82B20

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Table of Contents


Chapters

  • Introduction
  • Chapter 1. Definition of and statement of main result
  • Chapter 2. Deducing Theorem 1.2 from Theorem 2.1 and Proposition 2.2
  • Chapter 3. A determinant formula for
  • Chapter 4. An exact formula for
  • Chapter 5. Asymptotic singularity and Newton's divided difference operator
  • Chapter 6. The asymptotics of the entries in the -part of
  • Chapter 7. The asymptotics of the entries in the -part of
  • Chapter 8. The evaluation of
  • Chapter 9. Divisibility of by the powers of and
  • Chapter 10. The case of Theorem 8.1, up to a constant multiple
  • Chapter 11. Divisibility of by the powers of
  • Chapter 12. Divisibility of by the powers of
  • Chapter 13. The proofs of Theorem 2.1 and Proposition 2.2
  • Chapter 14. The case of arbitrary slopes
  • Chapter 15. Random covering surfaces and physical interpretation
  • Appendix. A determinant evaluation