Geodesic
Random matrices, magic squares and matching polynomials
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zeta-function, and by theoretical physicists in connection with Quantum Chaos. In particular, Haake and collaborators have computed the variance of the coefficients of these polynomials and raised the question of computing the higher moments. The answer turns out to be intimately related to counting integer stochastic matrices (magic squares). Similar results are obtained for the moments of secular coefficients of random matrices from orthogonal and symplectic groups. Combinatorial meaning of the moments of the secular coefficients of GUE matrices is also investigated and the connection with matching polynomials is discussed.
DOI : 10.37236/1859
Classification : 05A15, 05E05, 05E10, 11M06, 15B52, 60B11, 60B15, 15B51, 05B15
Mots-clés : characteristic polynomial of random matrix, moments of secular coefficients, counting magic squares, secular coefficients of GUE matrices 
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     author = {Persi Diaconis and Alex Gamburd},
     title = {Random matrices, magic squares and matching polynomials},
     journal = {The electronic journal of combinatorics},
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     number = {2},
     doi = {10.37236/1859},
     zbl = {1050.05011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1859/}
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Persi Diaconis; Alex Gamburd. Random matrices, magic squares and matching polynomials. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1859

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