论文标题
关于有限图的弹道沉积模型的生长
On the Growth of a Ballistic Deposition Model on Finite Graphs
论文作者
论文摘要
我们重新审视Atar，Athreya和Kang引入的弹道沉积过程。令$ \ Mathcal {g} =（v，e）$为有限的连接图。我们在$ \ Mathcal {G} $中独立和统一的顶点选择。如果选择了顶点$ x $，并且先前的高度配置由$ h =（h_y）_ {y \ in v} \ in \ mathbb {n} _0^v $，则高度$ h_x $由\ [\ tilde {\ tilde {h} _x _x _x：= 1 + max _ y \ sim = y \ sim fy \ [\ tilde tilde {\ tilde {\ tilde { \]我们研究了该增长模型的渐近特性。我们确定某些图的渐近生长参数$γ（\ Mathcal {g}）$，并证明波动左右$γ（\ Mathcal {G}）$的中心限制定理。我们还给出了Atar等人获得的不平等的新图理论解释。
We revisit a ballistic deposition process introduced by Atar, Athreya and Kang. Let $\mathcal{G}=(V,E)$ be a finite connected graph. We choose independently and uniformly vertices in $\mathcal{G}$. If a vertex $x$ is chosen and the previous height configuration is given by $h=(h_y)_{y \in V} \in \mathbb{N}_0^V$, the height $h_x$ is replaced by \[ \tilde{h}_x := 1 + \max_{y \sim x} h_y. \] We study asymptotic properties of this growth model. We determine the asymptotic growth parameter $γ(\mathcal{G} )$ for some graphs and prove a central limit theorem for the fluctuations around $γ( \mathcal{G})$. We also give a new graph-theoretic interpretation of an inequality obtained by Atar et al..
