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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.

Keywords

Brownian Motion Euclidean Space Random Process Conditional Distribution Brownian Bridge 
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References

  1. 1.
    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
  3. 3.
    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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