On the Growth of a Ballistic Deposition Model on Finite Graphs

We revisit a ballistic deposition process introduced by Atar et al. in [2]. Let J = (V, E) be a finite connected graph and choose independently and uniformly vertices in g. If a vertex x is an element of V gets chosen and the previous height configuration is h = (h(y))(y is an element of V) is an element of N-0(V), the height h(x) is replaced by (h) over tilde (x) := 1 + max(y similar to x )h(y). For different underlying graphs g, we determine the asymptotic growth parameter gamma(g) of this model. We also present a central limit theorem for the height fluctuations around gamma(g) and a graph-theoretic reinterpretation of an inequality obtained in [2].