Capital letters
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g.tex
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g.tex
@ -480,7 +480,7 @@ This series can be rewritten
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where $\ket{I_0}=\ket{i_0}$ is the initial state, $n_0$ is the number of times the walker remains within the domain of $\ket{i_0}$ (with $1 \le n_0 \le N+1$), $\ket{I_1}$ is the first exit state that does not belong to $\cD_{i_0}$, $n_1$ is the number of times the walker remains in $\cD_{i_1}$ (with $1 \le n_1 \le N+1-n_0$), $\ket{I_2}$ is the second exit state, and so on.
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Here, the integer $p$ goes from 0 to $N$ and indicates the number of exit events occurring along the path.
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The two extreme cases, $p=0$ and $p=N$, correspond to the cases where the walker remains in the initial domain during the entire path, and to the case where the walker exits a domain at each step, respectively.
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\titou{In what follows, we shall systematically write the integers representing the exit states in capital letter.}
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\titou{In what follows, we shall systematically write the integers representing the exit states in capital letters.}
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%Generalizing what has been done for domains consisting of only one single state, the general idea here is to integrate out exactly the stochastic dynamics over the
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%set of all paths having the same representation, Eq.(\ref{eff_series}). As a consequence, an effective Monte Carlo dynamics including only exit states
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