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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

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2: 16.24 Physical Applications

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§16.24(i) Random Walks

… ►They are also potentially useful for the solution of more complicated restricted lattice walk problems, and the 3D Ising model; see Barber and Ninham (1970, pp. 147–148). …

3: Bibliography D

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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach. Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical Sciences, New York.

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ISBN 0-9658703-2-4; 0-8218-2695-6, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§18.38(ii), §18.38(ii).

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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.

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ISSN 0010-3640, Document, MathReview (D. S. Lubinsky), ZentralBlatt

Referenced by:

§18.32.

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Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.

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External Links:

Document

Referenced by:

§15.18.

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$2$D gravity and random matrices. Phys. Rep. 254 (1-2), pp. 1–133.

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ISSN 0370-1573, Document, MathReview (Yolanda Lozano)

Referenced by:

§32.16.

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Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.

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Referenced by:

§18.38(iii).

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4: Bibliography B

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On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (4), pp. 1119–1178.

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ISSN 0894-0347, FullText, MathReview (David J. Aldous), ZentralBlatt

Referenced by:

§32.14.

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Random and Restricted Walks: Theory and Applications. Gordon and Breach, New York.

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External Links:

ZentralBlatt

Referenced by:

§16.24(i).

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Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.

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External Links:

Document, ZentralBlatt

Referenced by:

§36.14(iii), §9.16.

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Focusing and twinkling: Critical exponents from catastrophes in non-Gaussian random short waves. J. Phys. A 10 (12), pp. 2061–2081.

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External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§36.6.

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A class of solvable potentials. Nuovo Cimento (10) 25, pp. 864–879.

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External Links:

Document, MathReview (S. Rosendorff), ZentralBlatt

Referenced by:

§15.18.

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