We consider a percolation model on square lattices with sites weighted by beta-distributed random variables $S\sim \mathrm{Beta}(a,b)$ with a positive real parameters $a>0$ and $b>0$. Using the Monte Carlo method, we estimate the percolation probability $P_{\infty }$ as a relative frequency $P_{\infty }^{\ast }$ averaged over the target subset of sites on a square lattice. As a result of the comparative analysis, we formulate two empirical hypotheses: the first on the correspondence of percolation thresholds $p_c$ to $p_0$-quantiles (where level $p_0=0.592746\dots$ coincides with the percolation threshold for the site percolation model on a square lattice) of random variables $S_i$ weighing sites of the square lattice, and the second on the convergence of statistical estimates of percolation probability functions $P_{\infty }^{\ast }\left(p\right)$ to cumulative distribution functions $F_{S_i}\left(p\right)$ of these variables $S_i$ for the supercritical values of the occupation probability $p\ge p_c$.

我们考虑一个正方形网格上的渗流模型，其站点由β分布随机变量加权 $\mathrm{小号}〜\mathrm{贝塔}（\mathrm{一种}，b）$ 真实参数为正 $\mathrm{一种}>0$ 和 $b>0$。使用蒙特卡洛方法，我们估计渗滤概率$P_{\infty }$ 作为相对频率 $P_{\infty }^{\ast }$在方格上对目标的目标子集进行平均。作为比较分析的结果，我们提出了两个经验假设：第一个关于渗透阈值的对应关系$p_C$ 至 $p_0$-分位数（所在级别 $p_0=0。592746\dots$ 与随机变量的位置渗透模型的渗透阈值一致） ${\mathrm{小号}}_{\mathrm{一世}}$ 权重的方格，第二个关于收敛概率函数的统计估计的收敛 $P_{\infty }^{\ast }（p）$ 累积分布函数 $F_{{\mathrm{小号}}_{\mathrm{一世}}}（p）$ 这些变量中 ${\mathrm{小号}}_{\mathrm{一世}}$ 占位概率的超临界值 $p\ge p_C$。