Hello all,

I am taking a course on modelling and I have come across a concept in the textbook that I do not understand. In the text, an example introduces the concept of Gaussian correlation such as:

One can study condition number more systematically by simulation. Suppose we have a one-dimensional random process z with Gaussian correlation, parametrized by correlation length ξ:

z(ξ) ∼ P(ξ) 0 < ξ. (2.33) (P is the state covariance)

Suppose we randomly distort the elements of P with a symmetric perturbation:

P ̄(ξ)=P(ξ) (W WT) wij ∼N(0,σ2)

I am not sure what correlation length ξ actually IS in this case? I am aware of what a condition number is but not what correlation length ξ is.