The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions.
- 1st ed.
- 1 online resource (118 pages)
Intro -- Contents -- Abstract -- Introduction -- Chapter 1. Definition of ω 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 ω -- Chapter 4. An exact formula for U[sub(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 ς and q ς[sup(-1)] -- Chapter 10. The case q = 0 of Theorem 8.1, up to a constant multiple -- Chapter 11. Divisibility of det(dM[sub(0)]) by the powers of (x[sub(i)] x[sub(j)]) ς[sup(±1)](y[sub(i)] y[sub(j)]) ah -- Chapter 12. Divisibility of det(dM[sub(0)]) by the powers of (x[sub(i)] z[sub(j)]) ς[sup(±1)](y[sub(i)] ω[sub(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 -- Bibliography.