Limit laws and semistability on infinite-dimensional locally compact groups (Q2751511)

The limit behaviour of automorphism-normalized products of i.i.d. \(\mathbb G\)-valued random variables on certain infinite-dimensional groups \(\mathbb G\) is investigated. In contrast to the well understood case of finite-dimensional groups [see the author and \textit{E. Siebert}, ``Stable probability measures on Euclidean spaces and on locally compact groups'' (Kluver, 2001)], new and unexpected phenomena appear. The author does not obtain a general theory in case of infinite-dimensional groups \(\mathbb G\) rather than presents various illustrative examples. In particular, if \(\mathbb G=K^{\mathbb Z}\) for some compact Lie group \(K\), the author shows that there exists a semistable law on \(\mathbb G\) such that any projection to a finite product \(K^n\) is not semistable.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00042].