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[[math]]
\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}
[[math]]
yields:


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Questions and Remarks:


  • Q: What exactly mean Var(\xi_i)? Is it mean
?
A:

is the variance, essentially the square of the standard deviation (l' écart-type) of my data distribution - marcello.civelli marcello.civelli


  • Q: I am not sure to understand question I-2: are we suppose to do as if each step of the markovian walk gives a independent random variable (which is of course wrong: the position between two steps are correlated). ( Ok seems to be "yes" according to part II)



  • Q: I have a problem with the formula (1), namely the formula which gives the statistical error in our Markov chain data from the autocorrelation function. I would expect that we recover the usual formula ( sqrt(var/N) ) if the data are uncorellated (ie if C(n) = 0 for n > 0), but here I get sqrt(2var/N).
  • A: I guess one has to count for each n 2 possible distances between couples of sites, one in the positive, the other in the negative direction, hence a factor 2, except for the distance 0 point....I guess. Ask Alberto. - marcello.civelli marcello.civelli

  • A: Yes you are right, there is a small mistake in Eq.(1). The correct formula is - alberto.rosso alberto.rosso


- Shouldn't there be a minus sign in front of C(0) ?

Oups sorry I just realised you change the beginning of your sum, so this is completely equivalent...


- I don't know where to put this put the lecture class for this week is not online (even though the link exist, the corresponding page does not)
A: Link should be operational now - marcello.civelli marcello.civelli