Metropolis continues

For large $n$ we require that ${\cal w}^{(n\rightarrow \infty)}_i = p_i$, the desired probability distribution. Taking this limit, gives the balance requirement

$$\begin{equation} \sum_j \left [p_jT_{j\rightarrow i} A_{j\rightarrow i}-p_iT_{i\rightarrow j}A_{i\rightarrow j} \right ] = 0, \tag{7} \end{equation}$$

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