Geodesic
Biharmonic functions on groups and limit theorems for quasimorphisms along random walks
Björklund, Michael1 ; Hartnick, Tobias2
1 Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
2 Mathematics Department, Technion - Israel Institute of Technology, 32000 Haifa, Israel
Geometry & topology, Tome 15 (2011) no. 1, pp. 123-143.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 nondegenerate 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 quasimorphisms on countable groups we also obtain integral representations using martingale convergence.

DOI : 10.2140/gt.2011.15.123
Keywords: quasimorphism, central limit theorem, biharmonic function, random walks, bounded cohomology

Björklund, Michael 1 ; Hartnick, Tobias 2

1 Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
2 Mathematics Department, Technion - Israel Institute of Technology, 32000 Haifa, Israel 
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Björklund, Michael; Hartnick, Tobias. Biharmonic functions on groups and limit theorems for quasimorphisms along random walks. Geometry & topology, Tome 15 (2011) no. 1, pp. 123-143. doi : 10.2140/gt.2011.15.123. http://geodesic.mathdoc.fr/articles/10.2140/gt.2011.15.123/

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