Quenched CLT for random toral automorphism

Arvind Ayyer; Carlangelo Liverani; Mikko Stenlund

doi:10.3934/dcds.2009.24.331

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2009, Volume 24, Issue 2: 331-348. Doi: 10.3934/dcds.2009.24.331

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Quenched CLT for random toral automorphism

1.
Department of Physics, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854
2.
Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma
3.
Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854

Received: January 31, 2008

Revised: August 31, 2008

Published: May 2009

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Abstract

We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space specifically tailored to use the cone condition satisfied by the maps.

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Mathematics Subject Classification: 60F05, 37D20, 82C41, 82D30.

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