Random walks and kernel methods

Statistical Physics and Complexity Group meeting

Random walks and kernel methods

  • Event time: 11:30am until 12:30pm
  • Event date: 7th February 2018
  • Speaker: Anthony Wood (Formerly School of Physics & Astronomy, University of Edinburgh)
  • Location: Room 2511,

Event details

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.