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


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.


Statistical Physic Group Theory Initial Distribution Energy Problem 
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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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