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- W4320933037 abstract "We define the $L$-measure on the set of Dirichlet characters as an analogue of the Plancherel measure, once considered as a measure on the irreducible characters of the symmetric group. We compare the two measures and study the limit in distribution of characters evaluations when the size of the underlying group grows. These evaluations are proven to converge in law to imaginary exponentials of a Cauchy distribution in the same way as the rescaled windings of the complex Brownian motion. This contrasts with the case of the symmetric group where the renormalised characters converge in law to Gaussians after rescaling (Kerov Central Limit Theorem)." @default.
- W4320933037 created "2023-02-16" @default.
- W4320933037 creator A5048392115 @default.
- W4320933037 date "2017-01-16" @default.
- W4320933037 modified "2023-09-28" @default.
- W4320933037 title "Random characters under the $L$-measure, I : Dirichlet characters" @default.
- W4320933037 doi "https://doi.org/10.48550/arxiv.1701.04258" @default.
- W4320933037 hasPublicationYear "2017" @default.
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