Asymptotics of matrix integrals and tensor invariants of compact lie groups

Michael Stolz, Tatsuya Tate

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant-theoretic interpretation of this type of integral. For arbitrary regular irreducible representations of arbitrary connected semisimple compact Lie groups, we obtain an asymptotic formula for the trace of permutation operators on the space of tensor invariants, thus extending a result of Biane on the dimension of these spaces.

Original languageEnglish
Pages (from-to)2235-2244
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number6
Publication statusPublished - 2008 Jun


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