Algorithmic Randomness
Progress and Prospects

Surveys on recent developments in the theory of algorithmic randomness and its interactions with other areas of mathematics.

Johanna N. Y. Franklin (Edited by), Christopher P. Porter (Edited by)

9781108478984, Cambridge University Press

Hardback, published 7 May 2020

368 pages, 5 b/w illus. 3 tables
23.4 x 15.7 x 2.4 cm, 0.64 kg

The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

1. Key developments in algorithmic randomness Johanna N. Y. Franklin and Christopher P. Porter
2. Algorithmic randomness in ergodic theory Henry Towsner
3. Algorithmic randomness and constructive/computable measure theory Jason Rute
4. Algorithmic randomness and layerwise computability Mathieu Hoyrup
5. Relativization in randomness Johanna N. Y. Franklin
6. Aspects of Chaitin's Omega George Barmpalias
7. Biased algorithmic randomness Christopher P. Porter
8. Higher randomness Benoit Monin
9. Resource bounded randomness and its applications Donald M. Stull
Index.

Subject Areas: Databases [UN], Algorithms & data structures [UMB], Probability & statistics [PBT], Mathematical logic [PBCD]