Ulam's redistribution of energy problem: Collision transformations
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.
KeywordsStatistical Physic Group Theory Initial Distribution Energy Problem
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