Random walks and kernel methods
I will present a method of tackling a class of 2-D random walks. Using an example of a 2-D walker with 3 possible movements, I will outline a derivation of the full generating function for paths of various lengths and initial conditions, starting from a recursion relation. This is a somewhat unconventional method that exploits the symmetry of a `kernel'.
My own work is predominantly based around the totally asymmetric exclusion process, which relies on a mapping of the matrix product algebra to one such 2-D walk.
Reference: Bousquet-Mélou, M. and Mishna, M., 2010. Walks with small steps in the quarter plane. Contemp. Math, 520, pp.1-40.
This is a weekly series of informal talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..