The scaling limit of the correlation of holes on the triangular lattice with periodic boundary conditions / [electronic resource] Mihai Ciucu.

"Volume 199, number 935 (end of volume)."

Includes bibliographical references (p. 99-100).

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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