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Higher Dimensions

Chapter
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Part of the Lecture Notes in Statistics book series (LNS, volume 71)

Abstract

In this chapter the results of Chap. 3 are extended to physical systems with many degrees of freedom. Given a random vector X=(X1,..., Xn), the behavior of (iX)(mod 1) = ((tX1) (mod 1),..., (tXn)(mod 1)) is studied in detail in Sect.4.1. A necessary and sufficient condition for weak-star convergence of (tX)(mod 1) to a distribution uniform on [0, l]n, Un, as t tends to infinity, is established in Theorem 4.2 (Borel, Hopf, Kallenberg). The random vector (tX)(mod 1) converges to Un in the variation distance if and only if X has a density (Theorem 5.3).

Keywords

Random Vector Variation Distance Joint Density Initial Displacement Billiard Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Department of EconomicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Departamento de Ingeniería IndustrialUniversidad de ChileSantiagoChile

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