Publication: Ewens measures on compact groups and hypergeometric kernels
Ewens measures on compact groups and hypergeometric kernels
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Bourgade, P., Nikeghbali, A., & Rouault, A. (2011). Ewens measures on compact groups and hypergeometric kernels. In C. Donati-Martin, A. Lejay, & A. Rouault (Eds.), Séminaire de Probabilités XLIII (No. 2006; Issue 2006, pp. 351–377). Springer. https://doi.org/10.1007/978-3-642-15217-7_15
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The general topic of the article is the study of probability measures on the unitary group U(N) and its closed subgroups. The authors start from the Haar measure on a compact subgroup on U(N) and show that such distributed random matrix is a product of independent random reflections. The authors also decompose certain determinants of random matrices into products of independent simply-distributed random variables. More precisely, they discuss the decomposition of det(Id-U), where U is either orthogonal, or unitary, or symplectic rando
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Bourgade, P., Nikeghbali, A., & Rouault, A. (2011). Ewens measures on compact groups and hypergeometric kernels. In C. Donati-Martin, A. Lejay, & A. Rouault (Eds.), Séminaire de Probabilités XLIII (No. 2006; Issue 2006, pp. 351–377). Springer. https://doi.org/10.1007/978-3-642-15217-7_15