Correlations| Correlations |
General Concepts
* Correlation functions:
Given a stochastic process described by variables xi,
the correlation function between two variables xi and xj is
C(xi, xj):= 
xi xj
–
xi xj,
which vanishes if the variables are statistically uncorrelated.
> Related topics:
see number theory [continued
fractions].
Correlations in Physics > s.a. molecular
physics [branched polymers]; quantum correlations.
* In field theory: The
field-field 2-point correlation function is often identified with the Green
function for the theory; > s.a. N-point
functions.
* Origin of correlations:
In all non-quantum contexts, correlations arise from one of two mechanism,
either a first event influences a second one by sending information (encoded
in bosons or molecules or other physical carriers, depending on the particular
context), or the correlated events have some common causes in their common
past.
* Correlation length:
The length scale at which the overall properties of components of a many-body
system begin to differ markedly from those of
the whole; Or, the distance over which fluctuations of microscopic
degrees
of freedom are significantly correlated to each other (usually a few "interatomic
spacings").
@ General references: Rajagopal & Rendell qp/05 [density-matrix
formulation]; Torquato IECR-cm/06 [realizable,
random media]; Grudka et al a0802 [genuine
multipartite classical correlations].
@ Decay of correlations: Lavenda JMP(82);
Xu
et
al CSF(04)
[maps and chaos].
@ Related topics: Lenard CMP(73)
[statistical state determined by correlations]; Nigmatullin TMP(74)
[time correlation functions, calculation]
> In gravitation and cosmology:
see galaxy
distribution.
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send feedback and suggestions to bombelli at olemiss.edu – modified 2
jun
2009