PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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