# 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: Primary 82B23; Secondary 05A16, 60F99, 60K35, 82B20

### Table of Contents

**Chapters**

- Introduction
- Chapter 1. Definition of $\hat {\omega }$ 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 $\hat {\omega }$
- Chapter 4. An exact formula for $U_s(a, b)$
- Chapter 5. Asymptotic singularity and Newton’s divided difference operator
- Chapter 6. The asymptotics of the entries in the $U$-part of $M’$
- Chapter 7. The asymptotics of the entries in the $P$-part of $M’$
- Chapter 8. The evaluation of $\det (M”)$
- Chapter 9. Divisibility of $\det (M”)$ by the powers of $q - \zeta $ and $q - \zeta ^{-1}$
- Chapter 10. The case $q = 0$ of Theorem 8.1, up to a constant multiple
- Chapter 11. Divisibility of $\det (dM_0)$ by the powers of $(x_i - x_j) - \zeta ^{\pm 1}(y_i - y_j) - ah$
- Chapter 12. Divisibility of $\det (dM_0)$ by the powers of $(x_i - z_j) - \zeta ^{\pm 1}(y_i - \hat {\omega }_j)$
- 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