The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions.
Ciucu, Mihai.
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.
9781470405410
Scaling laws (Statistical physics).
Bethe-ansatz technique.
Tiling (Mathematics).
Statistical mechanics.
Electronic books.
QC174.85.S34 -- .C58 2009eb
530.13
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.
9781470405410
Scaling laws (Statistical physics).
Bethe-ansatz technique.
Tiling (Mathematics).
Statistical mechanics.
Electronic books.
QC174.85.S34 -- .C58 2009eb
530.13