**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.

宮部賢志（ミヤベケンシ）

**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.

**Download**

slide

Attached slides are in English.

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**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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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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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Unpublished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.

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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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**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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**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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**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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**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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**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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