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Weingarten function

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In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of moments over classical groups. Thjey were first studied by Weingarten (1978) who found their asymptotic behavior, and named by Collins (2003), who evaluated them explicitly for the unitary group. For orthogonal and symplactic groups they were evaluated by Collins & Śniady (2006).

References

  • Collins, Benoît (2003), "Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability", International Mathematics Research Notices (17): 953–982, doi:10.1155/S107379280320917X, ISSN 1073-7928, MR1959915{{citation}}: CS1 maint: unflagged free DOI (link)
  • Collins, Benoît; Śniady, Piotr (2006), "Integration with respect to the Haar measure on unitary, orthogonal and symplectic group", Communications in Mathematical Physics, 264 (3): 773–795, doi:10.1007/s00220-006-1554-3, ISSN 0010-3616, MR2217291
  • Weingarten, Don (1978), "Asymptotic behavior of group integrals in the limit of infinite rank", Journal of Mathematical Physics, 19 (5): 999–1001, doi:10.1063/1.523807, ISSN 0022-2488, MR0471696
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