Cyclic birth and death chains and a combinatorial conjecture
This will be a non-technical talk describing joint with Ander Holroyd and Alejandro Ramirez concerning a simple class of discrete-time random walks on $\mathbb{Z}$. Given a vector $(p_0,p_1,...,p_{m-1})$, let $X$ be the nearest-neighbour random walk on $\mathbb{Z}$ whose right step probability from $x$ is $p_{x \mod m}$. We will look at how the limiting velocity of $X$ is affected by reordering the entries of the vector, and conjecture which ordering minimises the velocity. This claim is implied by a simple conjecture in "combinatorial optimization."