Seminars & Colloquia Calendar
The distribution of path lengths on directed weighted graphs
Yotam Smilansky - Rutgers University
Location: Hill 705
Date & time: Thursday, 07 November 2019 at 2:00PM - 3:00PM
Abstract: We will consider paths on directed weighted graphs and discuss results on the asymptotic growth rate of various path counting and path probability functions. Our methods involve the study of the Laplace transforms of these counting functions, and we will see that under certain incommensurability assumptions on the lengths of closed paths in the graph we may apply the Wiener-Ikehara Tauberian theorem, which was originally developed in the context of the prime number theorem and the zeros of the Riemann zeta function. In addition, some applications of these results will be presented, including uniform distribution and related statistics of Kakutani sequences of partitions and summation over regions in Pascal's triangle.
Joint work with Avner Kiro and Uzy Smilansky