Dani, S. G. and McCrudden, M.
(2006)
*Convolution roots and embedding of probability measures on Lie groups.*
Advances in Mathematics.
ISSN 0001-8708
(In Press)

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## Abstract

We show that for a large class of connected Lie groups $G$, viz. from \emph{class} $\mathcal{C}$ described below, given a probability measure μ on $G$ and a natural number $n$, for any sequence $\{\nu_i\}$ of $n$th convolution roots of μ there exists a sequence $\{z_i\}$ of elements of G, centralising the support of μ, and such that $\{z_i \nu_i \z_i^{-1}\} is relatively compact; thus the set of roots is relatively compact ‘modulo’ the conjugation action of the centraliser of supp μ. We also analyse the dependence of the sequence $\{z_i\}$ on $n$. The results yield a simpler and more transparent proof of the embedding theorem for infinitely divisible probability measures on the Lie groups as above, proved in [S.G. Dani, M. McCrudden, Embeddability of infinitely divisible distributions on linear Lie groups, Invent. Math. 110 (1992) 237–261].

Item Type: | Article |
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Uncontrolled Keywords: | Probability measures; previous termConvolution rootsnext term; Infinite divisibility; Embedding |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 16 Nov 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/645 |

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