---
abstract: 'This work presents new asymptotic formulas for family of walks in Weyl chambers. The models studied here are defined by step sets which exhibit many symmetries and are restricted to the first orthant. The resulting formulas are very straightforward: the exponential growth of each model is given by the number of steps, while the sub-exponential growth depends only on the dimension of the underlying lattice and the number of steps moving forward in each coordinate. These expressions are derived by analyzing the singular variety of a multivariate rational function whose diagonal counts the lattice paths in question. Additionally, we show how to compute subdominant growth for these models, and how to determine first order asymptotics for excursions.'
address:
- 'Cheriton School of Computer Science, University of Waterloo, Waterloo ON Canada & U. Lyon, CNRS, ENS de Lyon, Inria, UCBL, Laboratoire LIP'
- 'Department of Mathematics, Simon Fraser University, Burnaby BC, Canada, V5A 1S6'
author:
- Stephen Melczer
- Marni Mishna
bibliography:
- 'bibl.bib'
title: Asymptotic lattice path enumeration using diagonals
---

Introduction {#sec:intro}
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The reflection principle and its various incarnations have been indispensable in the study of the lattice path models, particularly in the discovery of explicit 