For more information about this meeting, contact Stephen Simpson, Jan Reimann.
| Title: | Schnorr random pairs |
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| Seminar: | Logic Seminar |
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| Speaker: | Jason Rute, Pennsylvania State University |
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| Abstract: |
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| Algorithmic randomness uses computable techniques to robustly define a random real number. The most well know randomness notion is Martin-L"of randomness. In 1971 Schnorr criticized Martin-L"of randomness as being not effective enough. One of his suggested replacements was a notion of randomness now called Schnorr randomness. Schnorr randomness has many similar properties to Martin-L"of
randomness. However, at first, it seems that van Lambalgen's theorem, an important theorem about the randomness of pairs, fails for Schnorr randomness. However, by using a more uniform notion of randomness relative to an oracle, we can recover van Lambalgen's theorem for Schnorr randomness. I will present a proof of van Lambalgen's theorem for Schnorr randomness, which can be found in these two papers: K. Miyabe, Truth-table Schnorr and truth-table reducible randomness; K. Miyabe, J. Rute, Van Lambalgen's theorem for uniformly relative Schnorr and computable randomness. |
Room Reservation Information
| Room Number: | MB315 |
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| Date: | 09 / 17 / 2013 |
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| Time: | 02:30pm - 03:45pm |
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