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Letters in Mathematical Physics

, Volume 10, Issue 2–3, pp 149–153 | Cite as

Ulam's redistribution of energy problem: Collision transformations

  • David Blackwell
  • R. Daniel Mauldin
Article

Abstract

Ulam conjectured that for each given law of redistribution of energy, D, there corresponds a limiting distribution, C(D), the ‘collision transform’ of the given law such that if X is an initial distribution of energy, then the distributions of the iterates of X under redistribution, converge to C(D). We give examples of this behaviour and prove that Ulam's conjecture is correct in case all moments of X exists.

Keywords

Statistical Physic Group Theory Initial Distribution Energy Problem 
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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References

  1. 1.
    SohatJ. A. and TamarkinJ. D., ‘The Problem of Moments’, Amer. Math. Soc. Math. Surveys, Vol. 1, Amer. Math. Soc., New York, 1943, p. 20.Google Scholar
  2. 2.
    BillingsleyP., Probability and Measure, Wiley, New York, 1979, p. 344.Google Scholar

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • David Blackwell
    • 1
  • R. Daniel Mauldin
    • 2
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsNorth Texas UniversityDentonUSA

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