Speaker. Gage Bonner, Department of Atmospheric science, UM.

Title.  Growth of history-dependent random sequences

Abstract. History-dependent random sequences (HDRS) are sequences in which the distribution of the outcome of a given step depends non-trivially on the entire history of the process. HDRS have numerous applications in sciences such as in polymer physics where basic models of confined polymer chains in small enclosures consist of lattice sites which are occupied sequentially. The points evolve according to self-avoiding random walk, which is a kind of HDRS that remains an active area of research. We will take a short tour through the "zoo" of interesting HDRS, concluding with the so-called Ulam-Kac adder. The Ulam-Kac adder is an integer HDRS about which very little is known rigorously.

We will discuss some open conjectures related to its moments and limiting behavior and recent progress towards settling them.