For more information about this meeting, contact Stephen Simpson, Jan Reimann.

Title: | Schnorr random pairs |

Seminar: | Logic Seminar |

Speaker: | Jason Rute, Pennsylvania State University |

Abstract: |

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 |

Date: | 09 / 17 / 2013 |

Time: | 02:30pm - 03:45pm |