On the Growth of a Ballistic Deposition Model on Finite Graphs

2020/01/27 by Georg Braun, Braun, Georg · 1 citation
Mathematics · #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR #msc:60C05

paper · pdf · doi:10.48550/arxiv.2001.09836

24 pages

arxiv created 2020/01/27 · arxiv updated 2020/01/28

Abstract

We revisit a ballistic deposition process introduced by Atar, Athreya and Kang. Let G=(V,E) be a finite connected graph. We choose independently and uniformly vertices in G. If a vertex x is chosen and the previous height configuration is given by h=(h_y)_{y ∈ V} ∈ ℕ₀^V, the height h_x is replaced by h_x := 1 + max_{y ∼ x} h_y. We study asymptotic properties of this growth model. We determine the asymptotic growth parameter γ(G ) for some graphs and prove a central limit theorem for the fluctuations around γ( G). We also give a new graph-theoretic interpretation of an inequality obtained by Atar et al..

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