## Van Lambalgen’s Theorem for uniform Kurtz randomness

News
26 Jan 2013, the slides were uploaded.

Title
Van Lambalgen’s Theorem for uniform Kurtz randomness

Type
Talk
TITECH, 25 Jan 2013

slides

## Lowness for uniform Kurtz randomness

News
Mar, 2013, Accepted for the presentation in CiE and rejected to the publication in LNCS
15 Jan, 2013, Submitted to a Conference

Title
Lowness for uniform Kurtz randomness

Type
Accepted in informal electronic proceedings in CiE
with T. Kihara

Journal
Submitted

Abstract
We propose studying uniform Kurtz randomness, which is the uniform relativization of Kurtz randomness. One advantage of this notion is that lowness for uniform Kurtz randomness has many character- izations, such as those via complexity, martingales, Kurtz tt-traceability, and Kurtz dimensional measure.

preprint

The results in this paper will be appeared in another paper.

## Characterization of Kurtz randomness by a differentiation theorem

News
Dec 25, 2012, Published
Aug 8, 2012, Published online
July 12, 2012, Accepted with a minor revision
Dec 23, 2011, Need to fix it
Oct 18, 2011, Submitted to a Journal

Title
Characterization of Kurtz randomness by a differentiation theorem

Type
Fullpaper

Journal
Theory of Computing Systems: Volume 52, Issue 1 (2013), Page 113-132
The page in TOCS

Abstract
Brattka, Miller and Nies showed that some major algorithmic randomness notions are characterized via differentiability.
The main goal of this paper is to characterize Kurtz randomness by a differentiation theorem on a computable metric space.
The proof shows that characterization by integral tests plays an essential part and shows that how randomness and differentiation are connected.

preprint

## Computable measures in computable analysis

News
20 Dec 2012, the slides were uploaded.

Title
Computable measures in computable analysis

Type
Talk
JAIST 20 Dec 2012

Slides

## Van Lambalgen’s Theorem and Radon-Nikodym derivative

News
26 Oct 2012, the slides were uploaded.

Title
Van Lambalgen’s Theorem and Radon-Nikodym derivative

Type
Young Logician’s Gathering in Japan
23-25 Nov 2012
Nara Seisyounen Kaikan

Slides

## The law of the iterated logarithm in game-theoretic probability

News
15 Nov 2012, the revised slides were uploaded.
26 Oct 2012, the slides were uploaded.

Title
The law of the iterated logarithm in game-theoretic probability

Type
Fourth Workshop on Game-Theoretic Probability and Related Topics
12-14 Nov 2012
The University of Tokyo

Abstract
The Kolmogorov law of the iterated logarithm (LIL) (1929) provides the exact speed of the convergence of the sum of independent ran- dom variables under a condition. Subsequently, Hartman and Wintner (1941) showed that, in the case of i.i.d. random variables, the existence of a second moment is sufficient for the LIL. Shafer and Vovk (2001)
studied the Kolmogorov LIL in game-theoretic probability and asked the treatment of the Hartman and Winter LIL in game-theoretic prob- ability.
I present a new sufficient condition for the LIL in game-theoretic probability, which has a similar form to the Hartman and Winter LIL. The main idea is to add a little stronger hedges. This is the joint work with Akimich Takemura.

Slides

## An introduction to algorithmic randomness

News
15 Nov 2012, the revised slides were uploaded.
26 Oct 2012, the slides were uploaded.

Title
An introduction to algorithmic randomness

Type
Fourth Workshop on Game-Theoretic Probability and Related Topics
12-14 Nov 2012
The University of Tokyo

Slides

## Where is randomness?

News
2 Oct 2012, the slides were uploaded.

Title
Where is randomness?

Type
Talk at Math Lectures
13 Oct 2012
Kyoto University

Slides

## Natural properties that a randomness notion should have

News
21 Sep 2012, presented and the final slides were uploaded.
16 Sep 2012, the slides were uploaded.

Title
Natural properties that a randomness notion should have

Type
Talk at
The Mathematical Society of Japan
18-21 Sep 2012
Kyushu University

Abstract
s-mathsoc

## On the notion of randomness

News
20 Sep 2012, updated the slide and uploaded the lecture note.

Title
On the notion of randomness

Type
Talk at
Summer school of foundations of mathematics
4-7 Sep 2012
Tokyo Institute of Technology