"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"--
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Surveys on recent developments in the theory of algorithmic randomness and its interactions with other areas of mathematics.
| Preface |
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vii | |
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Key developments in algorithmic randomness |
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1 | (39) |
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Algorithmic randomness in ergodic theory |
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40 | (18) |
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Algorithmic randomness and constructive/computable measure theory |
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58 | (57) |
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Algorithmic randomness and layerwise computability |
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115 | (19) |
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Relativization in randomness |
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134 | (41) |
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Aspects of Chaitin's Omega |
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175 | (31) |
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Biased algorithmic randomness |
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206 | (26) |
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232 | (69) |
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Resource bounded randomness and its applications |
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301 | (48) |
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| Index |
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349 | |
Johanna N. Y. Franklin is an Associate Professor at Hofstra University in Hempstead, NY. She earned her Ph.D. from the Group in Logic and the Methodology of Science at the University of California, Berkeley and has held postdoctoral positions in Singapore, Canada, and the United States. Christopher P. Porter is an Assistant Professor of Mathematics at Drake University in Des Moines, IA. After receiving his Ph.D. in the joint program in mathematics and philosophy at the University of Notre Dame, Porter completed postdoctoral positions at the University of Paris 7 and the University of Florida.
