Randomness in a dynamical system

Title
Randomness in a dynamical system

Type
Talk

This talk is in DSC seminar (Dynamical Systems and Computation) at Hokkaido University in Hokkaido on Feb 14, 2011.

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slide
Attached slides are in English.

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Algorithmic randomness over general spaces

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.

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Understanding randomness

A Japanese journal “Susemi”, which means a seminar of mathematics, features randomness titled “understanding randomness” on the February number in 2011.

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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Unpublished

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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.

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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.

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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.

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slide
Attached slides are in Japanese.

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How much better can we predict the future: predictability and the limit.

Title
How much better can we predict the future: predictability and the limit.

Type
Talk

This talk was given for high school students.
The detail is in Japanese.

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Algorithmic randomness over general spaces

Title
Algorithmic randomness over general spaces

Type
Talk

This talk is in “Formal Systems and Computability Theory” as a RIMS research project in Kyoto in Japan on Sep 16, 2010.
This talk is based on the paper Algorithmic randomness over general spaces.

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slide
Attached slides are in English.
Attached slides are in English.

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Limit theorems on a computable topological space

Title
Limit theorems on a computable topological space

Type
Talk

This talk is in ALGI21 at Shiga in Japan on Sep 6, 2010
and is based on the paper A Random Sequence of Reals.

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slide
Attached slides are partially Japanese and almost English.

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Computable Topology and Randomness

Title
Computable Topology and Randomness

Type
Talk

This talk in Computable Analysis in Kyoto on Jul 26, 2010.

This talk is about basic of computable analysis and research talk based on the paper A Random Sequence of Reals.

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slide
Attached slides are partially Japanese and almost English.

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