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A NOTE ON RANDOM MATRIX INTEGRALS, MOMENT IDENTITIES, AND CATALAN NUMBERS

  • Nicholas M. Katz (a1)

Abstract

We relate Catalan numbers and Catalan determinants to random matrix integrals and to moments of spin representations of odd orthogonal groups.

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1. Gessel, I. and Viennot, X., Determinants, paths, and plane partitions. Preprint, 1989, http://www.cs.brandeis.edu/∼ira.
2. Katz, N. M. and Sarnak, P. C., Random Matrices, Frobenius Eigenvalues, and Monodromy (American Mathematical Society Colloquium Publications 45 ), American Mathematical Society (Providence, RI, 1999).
3. Keating, J. P. and Snaith, N. C., Random matrix theory and L-functions at s = 1/2. Comm. Math. Phys. 214(1) 2000, 5789.
4. Kedlaya, K. and Sutherland, A., Hyperelliptic curves, L-polynomials, and random matrices. In Arithmetic, Geometry, Cryptography and Coding Theory (Contemporary Mathematics 487 ), American Mathematical Society (Providence, RI, 2009), 119162.
5. Krattenthaler, C., Determinants of (generalised) Catalan numbers. J. Statist. Plann. Inference 140(8) 2010, 22602270.
6. Shapiro, L., A short proof of an identity of Touchard’s concerning Catalan numbers. J. Combin. Theory Ser. A 20 1976, 375376.
7. Sloane, N., The On-line Encyclopedia of Integer Sequences, https://oeis.org/.
8. Stanley, R., Catalan Numbers, Cambridge University Press (New York, 2015).
9. Touchard, J., Sur certaines équations fontionnelles. In Proceedings of the International Mathematical Congress (Toronto, 1924), Vol. 1, University of Toronto Press (1928), 465472.
10. Varadarajan, V. S., Supersymmetry for Mathematicians: an Introduction (Courant Lecture Notes in Mathematics 11 ), New York University, Courant Institute of Mathematical Sciences (New York, 2004) American Mathematical Society, Providence, RI.
11. Weyl, H., Classical Groups, Princeton University Press (Princeton, NJ, 1946).
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