About me:
I am a mathematician at the University of Bielefeld. My primary area of research is random matrix theory with
focus on the symmetric group. More precisely, my research combines probability theory, combinatorics and
complex analysis to obtain asymptotics of fundamental objects such as the cycles counts, the total number
of cycles and the characteristic polynomial with respect to different probability measures on the symmetric group.
Research interests
Random matrix theory, number theory representation theory, function theory, probability and combinatorics
Recent Preprints:
| Article |
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On the number of cycles in a random permutation
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| Author(s) |
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Kenneth Maples,
Ashkan Nikeghbali,
Dirk Zeindler, |
| Journal | : | Electronic Communications in Probability
| | DOI | : | 10.1214/ECP.v17-1934 |
| Year |
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2012 |
| Abstract |
:
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We show that the number of cycles in a random permutation chosen according to
generalized Ewens measure is normally distributed and compute asymptotic
estimates for the mean and variance.
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| Article |
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The Characteristic Polynomial of a Random Permutation Matrix at Different Points, |
| Author(s) |
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Kim Dang and Dirk Zeindler, |
| Year |
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2011 |
| Abstract |
:
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We consider the logarithm of the characteristic polynomial of random
permutation matrices, evaluated on a finite set of different points. The
permutations are chosen with respect to the Ewens distribution on the symmetric
group. We show that the behavior at different points is independent in the
limit and are asymptotically normal. Our methods enables us to study more
general matrices, closely related to permutation matrices, and multiplicative
class functions.
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Article
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Random permutation matrices under the generalized Ewens measure,
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| Author(s) |
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Christopher Hughes,
Joseph Najnudel,
Ashkan Nikeghbali,
Dirk Zeindler, |
| Year |
: |
2011
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| Abstract |
: |
We consider a generalisation of the Ewens measure for the symmetric group,
calculating moments of the characteristic polynomial and similar multiplicative
statistics. In addition we study the asymptotic behaviour of linear statistics
(such as the trace of a permutation matrix or of a wreath product) under this
new measure.
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Full list of Publications, Visited Conferences and given Talks, Curriculum Vitae
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