Towards a Combinatorial Understanding of Lattice Path Asymptotics

Abstract

We provide a new strategy to compute the exponential growth constant of enumeration sequences counting walks in lattice path models restricted to the quarter plane. The bounds arise by comparison with half-planes models. In many cases the bounds are provably tight, and provide a combinatorial interpretation of recent formulas of Fayolle and Raschel (2012) and Bostan, Raschel and Salvy (2013). We discuss how to generalize to higher dimensions.

13 pages - technical correction from previous version

References in corpus (3)

• On 3-dimensional lattice walks confined to the positive octant
• Random Walks in Cones: the Case of Nonzero Drift
• On the exit time from a cone for random walks with drift

Cited by in corpus (1)

• Uniform Sampling and Visualization of 3D Reluctant Walks