约束度渗流模型中临界时间的单调性
On the monotonicity of the critical time in the Constrained-degree percolation model
摘要：
约束度渗流模型是在[B.N.B.德利马河Sanchis，D.C. dos Santos，V. Sidoravicius，and R.特奥多罗，斯托奇。过程Appl.（2020）]，其中证明了该模型在正方形晶格上具有非平凡的相变。我们研究了$d$维超立方晶格（$\mathbb{Z}^d$）上的约束度逾渗模型，并通过数值模拟发现，如果是$d=3,4$，则临界时间$t_{c}^{d}(k)$在约束$k$中是单调的，而不是增加的，就像当$d=2$时一样。我们验证了最低的约束值$k$，使系统表现出相变是$k=3$和相关临界指数$ν$的约束度渗流模型和普通伯努利渗流是相同的。
英文摘要：
The Constrained-degree percolation model was introduced in [B.N.B. de Lima, R. Sanchis, D.C. dos Santos, V. Sidoravicius, and R. Teodoro, Stoch. Process. Appl. (2020)], where it was proven that this model has a non-trivial phase transition on a square lattice. We study the Constrained-degree percolation model on the $d$-dimensional hypercubic lattice ($\mathbb{Z}^d$) and, via numerical simulations, found evidence that the critical time $t_{c}^{d}(k)$ is monotonous not increasing in the constrained $k$ if $d=3,4$, like it is when $d=2$. We verify that the lowest constrained value $k$ such that the system exhibits a phase transition is $k=3$ and that the correlation critical exponent $ν$ for the Constrained-degree percolation model and ordinary Bernoulli percolation are the same.
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