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Biharmonic functions on
groups and limit theorems for quasimorphisms along random
walks
Michael Björklund and Tobias Hartnick |
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Geometry & Topology 15 (2011) 123–143
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Abstract |
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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. |
Keywords
quasimorphism, central limit theorem, biharmonic function,
random walks, bounded cohomology
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Mathematical Subject Classification 2000
Primary: 20P05, 60F05
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References |
Publication
Received: 29 April 2010
Revised: 3 November 2010
Accepted: 24 August 2010
Published: 25 January 2011
Proposed: Danny Calegari
Seconded: Leonid Polterovich, Benson Farb
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Authors |
| Michael Björklund | |
| Departement Mathematik ETH Zürich Rämistrasse 101 8092 Zürich Switzerland |
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| Tobias Hartnick | |
| Mathematics Department Technion - Israel Institute of Technology 32000 Haifa Israel |
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