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random potentials


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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
2: 16.24 Physical Applications
§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
  • P. A. Deift (1998) 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.
  • P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou (1999b) 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.
  • L. Dekar, L. Chetouani, and T. F. Hammann (1999) Wave function for smooth potential and mass step. Phys. Rev. A 59 (1), pp. 107–112.
  • P. Di Francesco, P. Ginsparg, and J. Zinn-Justin (1995) 2 D gravity and random matrices. Phys. Rep. 254 (1-2), pp. 1–133.
  • R. Dutt, A. Khare, and U. P. Sukhatme (1988) Supersymmetry, shape invariance, and exactly solvable potentials. Amer. J. Phys. 56, pp. 163–168.
  • 4: Bibliography B
  • J. Baik, P. Deift, and K. Johansson (1999) On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (4), pp. 1119–1178.
  • M. N. Barber and B. W. Ninham (1970) Random and Restricted Walks: Theory and Applications. Gordon and Breach, New York.
  • M. V. Berry (1966) Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.
  • M. V. Berry (1977) Focusing and twinkling: Critical exponents from catastrophes in non-Gaussian random short waves. J. Phys. A 10 (12), pp. 2061–2081.
  • A. Bhattacharjie and E. C. G. Sudarshan (1962) A class of solvable potentials. Nuovo Cimento (10) 25, pp. 864–879.