Inventiones mathematicae

, Volume 104, Issue 1, pp 601–629

Intersecting random translates of invariant Cantor sets

  • Richard Kenyon
  • Yuval Peres

DOI: 10.1007/BF01245092

Cite this article as:
Kenyon, R. & Peres, Y. Invent. math. (1991) 104: 601. doi:10.1007/BF01245092


Given two Cantor setsX andY in [0, 1), invariant under the mapxb x mod 1, the Hausdorff dimension of (X+t)∩Y is constant almost everywhere. WhenX,Y are defined by admissible digits in baseb, and more generally by sofic systems, we compute this dimension in terms of the largest Lyapunov exponent of a random product of matrices. The results are extended to higher dimensions and multiple intersections.

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Richard Kenyon
    • 1
  • Yuval Peres
    • 2
  1. 1.IHESBures-sur-Y vetteFrance
  2. 2.Mathematics InstituteHebrew University of JerusalemIsrael

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