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The number of cycles in a random permutation and the number of segregating sites jointly converge to the Brownian sheet

Oberseminar Darmstadt

Datum: 24.01.2019

Zeit: 16:15–17:15 Uhr

Abstract: We study two random models: i) the number of cycles K(n) in a random Ewens(theta) permutation of n elements, and b) the number S(n) of segregating sites of a sample of size n governed by Kingman's coalescent with mutation rate theta/2.

A coupling is provided for these two models that allows us to deduce our main result: the vector (K(n), S(n)), properly rescaled, converges to a two-dimensional Brownian sheet on the unit square.


Dr. Helmut Pitters, Universität Mannheim


TU Darmstadt S2|15 Raum 401
Schlossgartenstr. 7, 64289 Darmstadt


Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381


Goethe-Universität Frankfurt am Main, Johannes Gutenberg Universität Mainz

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