SFU Discrete Math Seminar: Marni Mishna

  • Date: 10/18/2016
  • Time: 13:30
Lecturer(s):
Marni Mishna, SFU
Location: 

Simon Fraser University

Topic: 

Universality classes for weighted lattice paths: where probability and ACSV meet

Description: 

Lattice paths are very classic objects in both probability theory and enumerative combinatorics. In particular, weighted models bridge the gap between the two approaches very neatly. We consider an example, the Gouyou-Beauchamps model of lattice walks in the first quadrant, and discuss how to determine asymptotic enumeration formulas parameterized by the weights. The major tool is the theory of analytic combinatorics in several variables (ACSV) and we identify six different kinds of asymptotic regimes (called universality classes) which arise according to the values of the weights. Because we are able to explicitly and generically compute the constants of the asymptotic formula, we can determine a formula for a family of discrete harmonic functions.

Work in collaboration with Julien Courtiel, Stephen Melczer, and Kilian Raschel.

Other Information: 

Location: SCK 9509

 

This seminar is an on-going activity for the CRG on Applied Combinatorics. 

 

 

 

Final scientific report available here.