Abstract ....................................................... ix
Introduction .................................................... 1
Chapter 1. Definition of ŵ and statement of main result ........ 5
Chapter 2. Deducing Theorem 1.2 from Theorem 2.1 and
Proposition 2.2 .................................... 11
Chapter 3. A determinant formula for ŵ ........................ 15
Chapter 4. An exact formula for Us(α, b) ...................... 19
Chapter 5. Asymptotic singularity and Newton's divided
difference operator ................................ 27
Chapter 6. The asymptotics of the entries in the U-part of
M' ................................................. 37
Chapter 7. The asymptotics of the entries in the P-part of
M' ................................................. 41
Chapter 8. The evaluation of det(M'') ......................... 49
Chapter 9. Divisibility of det(M'') by the powers of q — ζ
and q — ζ-1 ........................................ 53
Chapter 10. The case q = 0 of Theorem 8.1, up to a constant
multiple ........................................... 57
Chapter 11. Divisibility of det(dMo) by the powers of
(xi — xj) - ζ±1(yi -yj) - αh ........................ 61
Chapter 12. Divisibility of det(dM0) by the powers of
(xi — zj) — ζ±1(yi — Wj) ............................ 67
Chapter 13. The proofs of Theorem 2.1 and Proposition 2.2 ...... 73
Chapter 14. The case of arbitrary slopes ....................... 75
Chapter 15. Random covering surfaces and physical
interpretation ..................................... 81
Appendix. A determinant evaluation ............................. 87
Bibliography ................................................... 99
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