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Is there a book that goes deep into correlation functions? What I'm interested in a book/article that explains in the detail the relation of the correlation functions with symmetries and how one can understand the link between the use of correlation functions and measurements in the lab. I am interested in experimental examples/theory not restricted to quantum, but all kind of physics examples that use correlation function.

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Does this help?

Hydrodynamic Fluctuations, Broken Symmetry, And Correlation Functions

I learnt a lot from it.

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Thanks, It seems good. –  Caraiani Claudiu Feb 29 '12 at 14:50
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L.E. Reichl, A modern course in statistical physics,

combines the theory with lots of applications form different fields,and shows how correlations are used to calculate the coefficients in various hydrodynamic euqations and transport equations form first principles.

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One of the questions that I was interested is the following case: say you have two random variables and and a certain corellation between them. Say you add to a certain variable an additive noise,how is the correlation affected? –  Caraiani Claudiu Mar 4 '12 at 4:17
    
In the simplest case not at all: z=y+eps, <eps>=0 with eps uncorrelated with x implies corr(x,z)=<(x-xbar)(z-zbar)>=<(x-xbar)(y-ybar)+eps>=corr(x,y)+0. –  Arnold Neumaier Mar 4 '12 at 11:31
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