Commit 30f1345b authored by Michael Wimmer's avatar Michael Wimmer
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try to fix list formatting

parent 65e73c82
Pipeline #57567 passed with stages
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......@@ -129,11 +129,12 @@ As for all approximate importance sampling techniques, the Rosenbluth method run
To overcome this imbalance in weights, [Grassberger](https://doi.org/10.1103/PhysRevE.56.3682) introduced a pruning and enriching steps to the Rosenbluth method to improve balance.
In particular, after adding a subunit to a polymer such that the current length is $L'$, the following two steps are performed for every polymer $k$:
1. *Pruning*: If the weight $w_k^{(L')} < W_-^{(L')}$$, one of the following two actions is performed. Which of the two is performed is chosen randomly with equal probability (i.e. (a) with probability $1/2$ and (b) with probability $1/2$)
a. the polymer $k$ is discarded.
That means the current polymer length $L'$ is discarded and not used to grow further. However, the previous lengths of the polymer $k$ are still used for the averages for length $<L'$.
a. the polymer $k$ is discarded.
That means the current polymer length $L'$ is discarded and not used to grow further. However, the previous lengths of the polymer $k$ are still used for the averages for length $<L'$.
b. The weight $w_k^{(L')}$ is doubled: $w_k^{(L'), \text{new}} = 2 w_k^{(L')}$.
This new weight is used to compute the average for length $L'$ and used to compute the weight of the polymer when grown further: e.g. if in the next step there are $m_{k, L'+1}$ possibilities to place the subunit, $w_k^{(L'+1)} = m_{k, L'+1}\, w_k^{(L'), \text{new}}$, etc.
This new weight is used to compute the average for length $L'$ and used to compute the weight of the polymer when grown further: e.g. if in the next step there are $m_{k, L'+1}$ possibilities to place the subunit, $w_k^{(L'+1)} = m_{k, L'+1}\, w_k^{(L'), \text{new}}$, etc.
2. *Enrichment*: If the weight $w_k^{(L')} > W_+^{(L')}$, the polymer is copied, i.e. a second copy of this polymer is added for length $L'$. The original and the copy are assigned half of the original weight, these new weights and used for all computations of averages of length $L'$ and larger.
### Why does PERM work?
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