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1 results

  • Loi des grands nombres pour des sommes de Riesz–Raikov multidimensionnelles

  • EMMANUEL LESIGNE
  • Journal:
    Compositio Mathematica / Volume 110 / Issue 1 / January 1998
    Published online by Cambridge University Press:
    04 December 2007, pp. 39-49
    Print publication:
    January 1998
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  • Let A and x be d × d and d × 1 real matrices. We study the asymptotic distribution of the sequence ((A$^n$x) mod.Z$^d$) in the torus $T^d$. We prove that for any A, for almost all x, this distribution exists; we characterize the case where this distribution is uniform; we give a description of the non uniform case. Finally we ask a question on the asymptotic distribution modulo 1 of the coefficients of the sequence of powers (A$^n$).