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1:50 AM
Emilio, plz halp
0
Q: Probability density for a Markov process with Gaussian two point functions

DanielSankThe problem Consider a stochastic process with the following three properties: The process is Markov, meaning that $p(x_n,t_n|x_{n-1},t_{n-1},\ldots x_1, t_1) = p(x_n,t_n|x_{n-1},t_{n-1}).$ The conditional probability is $$p(x_n, t_n|x_{n-1},t_{n-1}) = \left[ 2 \pi \sigma^2 (1 - e^{-2 \gamma (t_...

 
 
6 hours later…
7:46 AM
When one reads a popular science book how much of the stuff actually gets stored in brain. Any or none? Do I have to read several times? Does anybody do that?
@JohnRennie !
 
8:23 AM
I guess it’s just for fun! Nothing fruit ful can be achieved by it!
I was reading about force fields of michio kaku.
 
 
3 hours later…
fqq
11:39 AM
@DanielSank the exponent is a sum of quadratic terms so it's a quadratic form in $\mathbf{x}$. It must be positive definite and the prefactor must be right because it's a probability distribution
if you want to check it explicitly you don't actually have to sum that many terms, just extract the non-zero matrix elements. If I have time later I'l write an answer
 
 
4 hours later…
3:56 PM
Can I understand somehow why continuos phase transitions are characterized by correlation functions with power law behaviour near the critical point? I know continuos phase transitions are characterised by non analitycities in the thermodinamic potentials' derivatives (order 2 or greater)...
On the other hand correlation functions (es spin-spin) are the moments (or cumulants) of the generating function. To get the power law behaviour I must find that these correlation functions are the Fourier transform of a non analytic function (othervise the space x correlation function would decrease exponentially, as it does far from the critical point)
The bridge between the two statements I guess is that the derivatives of the termodinamic potentials are the cumulants of the generating function. But these cumulants to me give the space x correlation function and not it's fourier transform in k-space which has the non analyticities. Am I saying some non sense? is there something I can look up for some formal argument about this question?
 
 
6 hours later…
9:45 PM
@fqq "Just extract the non-zero matrix elements". Right but now?
 
10:33 PM
In quantum ensembles, is one of the constraints conservation of energy?
As in $E$ is a constant
or do we say $\langle E \rangle$ is a constant?
 

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