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ON THE PROBABILITY DISTRIBUTION OF THE PRODUCT OF POWERS OF ELEMENTS IN COMPACT LIE GROUPS

Part of: Probabilistic methods in group theory Abstract harmonic analysis

Published online by Cambridge University Press:  17 May 2019

VU THE KHOI Open the ORCID record for VU THE KHOI [Opens in a new window]
VU THE KHOI*
Affiliation:
Institute of Mathematics, VAST, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam email vtkhoi@math.ac.vn
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Abstract

In this paper, we study the probability distribution of the word map $w(x_{1},x_{2},\ldots ,x_{k})=x_{1}^{n_{1}}x_{2}^{n_{2}}\cdots x_{k}^{n_{k}}$ in a compact Lie group. We show that the probability distribution can be represented as an infinite series. Moreover, in the case of the Lie group $\text{SU}(2)$, our computations give a nice convergent series for the probability distribution.

Keywords

probability distributionword mapscompact Lie groups

MSC classification

Primary: 20P05: Probabilistic methods in group theory
Secondary: 43A80: Analysis on other specific Lie groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 3 , December 2019 , pp. 440 - 445
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2015.20.

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