Geodesic
The asymptotics of reflectable weighted walks in arbitrary dimension
Marni Mishna1 ; Sam Simon1 ; Marni Mishna ; Sam Simon
1Department of Mathematics Simon Fraser University, Burnaby, BC, Canada
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 955-962 
Marni Mishna; Sam Simon; Marni Mishna; Sam Simon. The asymptotics of reflectable weighted walks in arbitrary dimension. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 955-962. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a92/
@article{AMUC_2019_88_3_a92,
     author = {Marni Mishna and Sam Simon and Marni Mishna and Sam Simon},
     title = { The asymptotics of reflectable weighted walks in arbitrary dimension},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {955--962},
     year = {2019},
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     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a92/}
}
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Voir la notice de l'article provenant de la source Comenius University

We consider the weighted lattice walks with a reflectable step set restricted to the positive $d$-dimensional orthant. We obtain asymptotic formulas for the number of such walks as a function of the weights. To do so, we set up the desired generating function as the diagonal of a rational function. Then we perform a coefficient extraction via an integral computation which is broken up into two cases. One part uses the residue theorem to evaluate the integral within an error, while the other uses known approximations of Fourier-Laplace integrals.