# Dynamic Monte-Carlo algorithms_Questions

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You can insert math formulæ using LaTeX code: e.g. typing
[[math]]
\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}
[[math]]
yields:
$\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}$

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## Questions and Remarks:

• Q: In question 4, we need to find the correlation function defined as a mean, but it's not very clear over what this mean in taken; I would take it over the thermal equilibrium but we're studying the dynamics so I'm confused.
• A: In question 4, it is precised : «You have the freedom to chose the initial condition (e.g. fixed direction, or distributed with the equilibrium distribution), but be consistent: choose the same for the analytical computation and for the numerical evaluation.» It means that the randomness to average when measuring C(tt) is twofold:
- in the initial condition, drawn from an initial distribution (fixed spin, or spin drawn from the equilbrium distribution, as mentionned)
- and in the dynamics (i.e. the runs of your algorithm).
- Vivien.Lecomte Nov 29, 2014

• Q: in Q4, what do you mean by tranfer matrix? Are you referring to the Markov matrix Mab = p(b->a)?
• A: indeed, we called this matrix the Markov matrix in Tutorial this year. It is called (up to a transposition) the transfer matrix in the SMAC book.
- Vivien.Lecomte Dec 4, 2014