$0$                  $0$           …        $\times$            $\times$
                                                                                            
    $\mu^{(d-1)}_{a}$            $0$                  $0$           …        $\times$            $\times$
     $\mu^{(d)}_{a}$             $0$               $\times$         …        $\times$            $\times$

As in the previous Section we will need first some limits of correlation functions.

The limit of correlation functions
----------------------------------

\[teh50\]a) For any $y_1,\dots ,y_{d-k}\in Y$ with different orientations we have $$\label{dals}
\lim_{a\rightarrow\infty}\rho_{d-k}(y_{1},\ldots,y_{d-k};\mu_{a}^{(d)}) = \frac{k}{d},\;k=1,\ldots,d-1.$$ b) For all sets of $2(d-k)$ arguments which fullfil that each facet of $\{ y_{1},\ldots,y_{d-k} \}$ has different orientation and the same applies to $\{ y_{d-k+1},\ldots,y_{2(d-k)} \}$ and there is $l$ common orientations within these two groups, then $$\label{teh52}\lim_{a\rightarrow\infty}\rho_{2(d-k)}(y_{1},\ldots,y_{2(d-k)};\mu_{a}^{(d)})=\frac{2k-d+l}{d}.$$ c) Consider $2(d-k)-1$ arguments such that each facet of $\{ y_{1},\ldots,y_{d-k} \}$ has different orientation and the same applies to $\{ y_{d-k+1},\ldots,y_{2(d-k)-1},y_1 \}.$ Let us have $l$ common orientations $e_{2},\ldots,e_{l+1}$ within these two groups of arguments not including orientation $e_{1}$ of $y_{1}$, then $$\label{teh53}\lim_{a\rightarrow\infty}\rho_{2(d-k)-1}(y_{1},\ldots,y_{2(d-k)-1};\mu_{a}^{(d)})=\frac{2k-d+l-1}{d}.$$

[**Proof**]{} a) Consider fixed facets $y_{1}, \ldots, y_{d-k}$ each associated with a different normal orientation vector, without loss of generality $e_{1}, \ldots, e_{d-k}.$ Then the correlation function can be expressed analogously to Lemma \[ll1\] as follows: $$\rho_{d-k}(y_{1},\ldots,y_{d-k};\mu_{a}^{(d)}) = \frac{\tilde{A}(a)}{\tilde{B}(a)},\qquad\tilde{A}(a)=$$ $$= \sum_{n=0}^{\infty}\frac{a^n}{n!}\int_{Y} \ldots \int_{Y} exp \left( \frac{\nu_{d}}{d!} \sum_{\substack{(x_{1},\ldots,x_{d}) \subset\\ \{u_{1},\ldots,u_{n},y_{1},\ldots,y_{d-k} \} }} \mathbb{H}^{0}(\cap_{i=1}^{d}x_{i}) \right)   \lambda^n({\text{\rm d}}(u_{1}, \ldots , u_{n})),$$ $\tilde{B}(a)=$$$= \sum_{n=0}^{\infty}\frac{a^n}{n!}\int_{Y} \ldots \int_{Y} exp \left( \frac{\nu_{d}}{d!} 