Biharmonic functions on groups and limit theorems for quasimorphisms along random walks
Group Theory
2015-03-17 v2 Probability
Abstract
We show for very general classes of measures on locally compact second countable groups that every Borel measurable quasimorphism is at bounded distance from a quasi-biharmonic one. This allows us to deduce non-degenerate central limit theorems and laws of the iterated logarithm for such quasimorphisms along regular random walks on topological groups using classical martingale limit theorems of Billingsley and Stout. For quasi-biharmonic quasimorphism on countable groups we also obtain integral representations using martingale convergence.
Cite
@article{arxiv.1005.0077,
title = {Biharmonic functions on groups and limit theorems for quasimorphisms along random walks},
author = {Michael Björklund and Tobias Hartnick},
journal= {arXiv preprint arXiv:1005.0077},
year = {2015}
}
Comments
18 pages, revised version. Main theorems have been extended to general topological groups, and not necessarily symmetric measures