Members of Random Closed Sets

Abstract. The members of Martin-L¨of random closed sets under a distribution studied by Barmpalias et al. are exactly the infinite paths through Martin-L¨of random Galton-Watson trees with survival parameter 2 3 . To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than γ = log2 3 2 , and a necessary condition is to have effective Hausdorff dimension greater than or equal to γ.

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: David Diamondstone, Bjørn Kjos-Hanssen
• Keywords: Applied Computing, CIE 2009, Effective Hausdorff Dimension, Martin-L¨of Random, Random Closed Sets