Bivariate Uniqueness and Endogeny for Recursive Distributional Equations : Two Examples

Details Bivariate Uniqueness and Endogeny for Recursive Distributional Equations : Two Examples Bivariate Uniqueness and Endogeny for Recursive Distributional Equations : Two Examples

2004-07-10

arxiv.org/abs/math/0407175v2

Mathematics

Probability

This paper has been withdrawn

Scientific paper

This paper has been withdrawn by the author because of finding a flaw in the proof of endogeny for the Frozen Percolation RDE which was one of two examples discussed in this paper. The other example is correct and can be obtained from the work "Bivariate Uniqueness and Endogeny for the Logistic Recursive Distributional Equation" of the author. At the current moment we believe that endogeny is false for the Frozen Percolation RDE. Fresh simulations done independently by the author and David J. Aldous suggest non-endogeny. Although a rigorous proof is yet to be found. It is interesting to note that one can prove that the tail of the associated Recursive Tree Process (RTP) is trivial. The work titled "A Necessary and Sufficient Condition for the Tail Triviality of a Recursive Tree Process" of the author present this result.

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