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Moments of characteristic polynomials enumerate two-rowed lexicographic arrays. (English) Zbl 1033.15017

Electron. J. Comb. 10, Research paper R24, 8 p. (2003); printed version J. Comb. 10, No. 3 (2003).
The author gives an interpretation of moments of characteristic polynomials of random unitary matrices in terms of counts of two-rowed lexicographic arrays whose weakly increasing subsequences have at most \(N\) elements. This connects the theory of these moments to last passage percolation theory, and gives a new interpretation of the conjecture J. P. Keating and N. C. Snaith [Commun. Math. Phys. 214, 57–89 (2000; Zbl 1051.11048)].

MSC:

15B52 Random matrices (algebraic aspects)
20G05 Representation theory for linear algebraic groups
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
11M06 \(\zeta (s)\) and \(L(s, \chi)\)

Citations:

Zbl 1051.11048
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