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Limiting-type theorem for conditional distributions of products of independent unimodular 2×2 matrices

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Abstract

We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as √t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments.

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Authors and Affiliations

  1. L. D. Landau Institute of Theoretical Physics, Academy of Sciences of USSR, Moscow

    S. K. Nechaev & Ya. G. Sinai

Authors
  1. S. K. Nechaev
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  2. Ya. G. Sinai
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Nechaev, S.K., Sinai, Y.G. Limiting-type theorem for conditional distributions of products of independent unimodular 2×2 matrices. Bol. Soc. Bras. Mat 21, 121–132 (1991). https://doi.org/10.1007/BF01237360

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  • DOI: https://doi.org/10.1007/BF01237360

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