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

Title: | Randomness, Riesz Capacity, Brownian Motion, and Complexity |

Seminar: | Logic Seminar |

Speaker: | Jason Rute, Penn State |

Abstract: |

- Algorithmic randomness is a topic in computability theory which investigates which paths in a stochastic process behave randomly (with respect to all computable statistical tests).
- Riesz capacity is an important concept in potential theory and stochastic processes. It is used to estimate the probability that an n-dimensional Brownian motion hits a given set or is zero on a given set of times.
- The a priori complexity KM(x) is a measure of the computational complexity of a finite bit string x.
I will present the following result which connects these three subjects. The following are equivalent for t in (0,1].
1) t is Martin-Löf random with respect to 1/2-Reisz capacity.
2) t is a zero of some Martin-Löf random one-dimensional Brownian motion.
3) sum_n 2^{n/2 - KM(t[0,…,n-1])} < \infty where t[0,…,n-1] is the first n bits of the binary expansion of t.
This is joint work with Joseph Miller. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 09 / 09 / 2014 |

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