Members of Random Closed Sets

Authors:
David Diamondstone;Bjørn Kjos-Hanssen
Affiliations:
Department of Mathematics, University of Chicago, Chicago IL 60615;Department of Mathematics, University of Hawai'i at Mānoa, Honolulu, HI, 96822
Venue:
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Year:
2009

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Abstract

The members of Martin-Löf random closed sets under a distribution studied by Barmpalias et al. are exactly the infinite paths through Martin-Löf random Galton-Watson trees with survival parameter $\frac{2}{3}$. To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than $\gamma=\log_2 \frac{3}{2}$, and a necessary condition is to have effective Hausdorff dimension greater than or equal to *** .