Title: The distribution of path lengths on directed weighted graphs. Abstract: We will consider paths on directed weighted graphs and discuss results on the asymptotic growth rate of various path counting functions. Our methods involve the study of the Laplace transforms of these counting functions, and we will see that under some incommensurability assumptions on the lengths of closed paths in the graph, the Wiener-Ikehara Tauberian theorem may be applied. 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.
Wed, 09/01/2019 - 12:00 to 13:00