Title
Algorithmic randomness over general spaces
Type
Talk
This talk is in CCA-CCR 2011 at Cape town in South Africa on Jan 31, 2011.
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slide
Attached slides are in English.
Understanding randomness
A Japanese journal “Susemi”, which means a seminar of mathematics, features randomness titled “understanding randomness” on the February number in 2011.
A Random Sequence of Reals
Since this paper was rejected by a Journal, I will divide the results, extend them and publish by some papers.
News
Jan 11, 2011, Rejected
Aug 2, 2010, Submitted to a Journal
Title
A Random Sequence of Reals
Type
Fullpaper
Journal
Unpublished
Download
preprint
Japanese summary
Abstract
We define a random sequence of reals as a random point on a computable topological space. This randomness has three equivalent simple characterizations, namely, by tests, by martingales and by complexity. We prove that members of a random sequence are relatively random. Conversely a relatively random sequence of reals has a random sequence such that each corresponding member is Turing equivalent. Furthermore strong law of large numbers and the law of the iterated logarithm hold for each random sequence.
Renewal
The following is a history of my site.
Dec 28,2010
The underlying system was changed to WordPress.
Sep 10,2010
The underlying system was changed to Drupal.
Sep 4, 2009
My website was first created by Haru.
Frequency and belief are probability
Title
Frequency and belief are probability
Type
Talk
This talk is in SLACS 2010 at Sendai in Japan on Nov 2, 2010.
Download
slide
Attached slides are in Japanese.