Asymptotic Analysis of a Paths Counting Problem

Asymptotic Analysis of a Paths Counting Problem

In this paper, we give a precise study of the asymptotic behaviour of the total number P_m,n of certain restricted lattice paths in an m*n grid of cells, which appeared in the context of counting train paths through a rail network. Our results are obtained by applying complex analytic techniques, namely the so called diagonalization method and the saddle point method and use the explicit formula for the bivariate generating function of P_m,n.

In this paper, we give a precise study of the asymptotic behaviour of the total number P_m,n of certain restricted lattice paths in an m*n grid of cells, which appeared in the context of counting train paths through a rail network. Our results are obtained by applying complex analytic techniques, namely the so called diagonalization method and the saddle point method and use the explicit formula for the bivariate generating function of P_m,n.