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Journal of the London Mathematical Society 2002 65(2):464-482; doi:10.1112/S0024610701002770
© 2002 by London Mathematical Society
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© The London Mathematical Society

A Central Limit Theorem for Magnetic Transition Operators on a Crystal Lattice

Motoko Kotani

Mathematical Institute, Graduate School of Sciences, Tohoku University Aoba, Sendai 980-8578, Japan, kotani{at}math.tohoku.ac.jp

Received 2 January 2001. Revision received 30 July 2001.

A central limit theorem for a generalized Harper operator on a crystal lattice is obtained. As the limit, the continuous semigroup of a uniform magnetic Schrödinger operator is captured on a vector space equipped with a special Euclidean structure. The standard realization of the crystal lattice is a key to the Euclidean structure and a linear vector potential on the Euclidean space from combinatorial data of the generalized Harper operator.


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