Convolution roots and embeddings of probability measures on lie groups

Dani, S. G. ; McCrudden, M. (2007) Convolution roots and embeddings of probability measures on lie groups Advances in Mathematics, 209 (1). pp. 198-211. ISSN 0001-8708

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00018...

Related URL: http://dx.doi.org/10.1016/j.aim.2006.05.002

Abstract

We show that for a large class of connected Lie groups G, viz. from class C described below, given a probability measure μ on G and a natural number n, for any sequence {vi} of th convolution roots of μ there exists a sequence {zi} of nth elements of G, centralising the support of μ , and such that {Ziν iZi-1}is relatively compact; thus the set of roots is relatively compact 'modulo' the conjugation action of the centraliser of suppµ. We also analyse the dependence of the sequence {zi} 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
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Probability Measures; Convolution Roots; Infinite Divisibility; Embedding
ID Code:8240
Deposited On:26 Oct 2010 12:06
Last Modified:16 May 2016 18:17

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