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

  • S. K. Nechaev
  • Ya. G. Sinai
Article

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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References

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    H. Fürstenberg,Noncommuting random products. Trans. Amer. Math. Soc.198, 3 (1963), 377–428.Google Scholar
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    V. N. Tutubalin,On limit theorems for the product of random matrices, Theory Prob. and Appl.10, 1 (1965), 15–27.Google Scholar
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    V. N. Tutubalin,Approximation of probability measures in variation and products of random matrices, Theory, Prob. and Appl.13, 1 (1968), 65–83.Google Scholar

Copyright information

© Sociedade Brasileira de Matemática 1991

Authors and Affiliations

  • S. K. Nechaev
    • 1
  • Ya. G. Sinai
    • 1
  1. 1.L. D. Landau Institute of Theoretical PhysicsAcademy of Sciences of USSRMoscow

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