Abstract: Given a cube in the lattice $\mathbb{Z}^3$ we consider the random walks from $(0,0,0)$ to $(n,n,n)$ such that only unit steps $(1,0,0), (0,1,0),(0,0,1)$ are possible. We study the number of times it hits the diagonal $(m, m, m)$ with $0<m\leq n$ and the sizes of the excursions. This problem can be approached using the composition scheme $V(W(z)) =\frac{1}{1-W(z)}$ considering the walk as a sequence of excursions.
The setting can be in fact generalized much more finding similar results for broader types composition schemes.
Gibbs partitions and lattice paths
13.10.2025 15:45 - 16:45
Organiser:
A. Carrance, M. Reibnegger
Location: