What is Correlation function: Definition and 51 Discussions

A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables are sometimes called cross-correlation functions to emphasize that different variables are being considered and because they are made up of cross-correlations.
Correlation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for interpolating values at points for which there are no observations.
Correlation functions used in astronomy, financial analysis, econometrics, and statistical mechanics differ only in the particular stochastic processes they are applied to. In quantum field theory there are correlation functions over quantum distributions.

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  1. ab_kein

    I Two-body correlation function computation

    I'm studying how to compute excess entropy in molecular dynamics (MD). I've found it is needed to compute the two-body correlation function (neglecting high-order terms), the details can be found, for example, in this article. So the definition of correlation function (CF for short) is ##C(t...
  2. gremory

    A Computing Correlation functions

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  3. T

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  4. W

    Coding of Spin Spin correlation function

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  5. Danny Boy

    A Quantum Ising model correlation function query

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  6. A

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  8. G

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  9. P

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  10. A

    I Why is there this extra term for this correlation function?

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  11. J

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  12. C

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  13. B

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  14. rocdoc

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  15. C

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  16. B

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  17. K

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  18. S

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  19. J

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  20. ChrisVer

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  21. S

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  22. S

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  23. T

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  24. P

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  25. enrikofermi

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  26. S

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  27. B

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  28. F

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  29. mhsd91

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  30. R

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  31. V

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  32. S

    Second-order correlation function

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  33. N

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  34. S

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  35. S

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  36. M

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  37. N

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  38. N

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    Please teach me this: Why the connected correlation functions depend on the x-y(the difference of two space-time coordinates of two points) only in case the expectation of field(<phi(x)>) is constant(the translation invariance of vacuum state). Thank you very much in advanced.
  39. N

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  40. T

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  41. M

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  42. 1

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  43. C

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  44. R

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  45. S

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  46. T

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  47. maverick280857

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  48. T

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  49. S

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  50. W

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