LIMIT THEOREMS ON THE DIRECT PRODUCT OF A NON-COMPACT LIE GROUP AND A COMPACT GROUP

G. Pap; Péter Major

doi:10.1556/sscmath.38.2001.1-4.21

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 38: Issue 1-4

LIMIT THEOREMS ON THE DIRECT PRODUCT OF A NON-COMPACT LIE GROUP AND A COMPACT GROUP

Authors:

G. Pap

G. Pap Please ask the editor of the journal.

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Péter Major

Péter Major Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics HU–1364 Budapest

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Pages:: 279–297

Online Publication Date:: 22 Jul 2005

Publication Date:: 01 May 2001

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.38.2001.1-4.21

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Let us consider a triangular array of random vectors (X (n) j; Y (n) j), n = 1;2;: : :, 1 5 j 5 kn, such that the first coordinates X (n) j take their values in a non-compact Lie group and the second coordinates Y (n) j in a compact group. Let the random vectors (X (n) j; Y (n) j) be independent for fixed n, but we do not assume any (independence type) condition about the relation between the components of these vectors. We show under fairly general conditions that if both random products Sn = kn Q j=1 X (n) j and Tn = kn Q j=1 Y (n) j have a limit distribution, then also the random vectors (Sn; Tn) converge in distribution as n !1 . Moreover, the non-compact and compact coordinates of a random vector with this limit distribution are independent.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

Online ISSN:: 1588-2896

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András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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