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This is probably a question whose answer should be available in some paper or textbook, but my searching for it hasn't helped me find a result that I could use.

The question is basically just what the title says. Let's say I have a stochastic process which is being drawn from the prior of a Gaussian process (i.e., I am not conditioning the process on any data or anything. I just have a random sample from the space of functions that the Gaussian process describes), and I treat that as my stochastic signal, then what is it's Rate Distortion like? In particular, I am interested in Gaussian processes with a squared exponential kernel.

In particular, I am interested in knowing what its Rate-distortion dimension is, and I believe I would need the Rate-distortion function to be able to calculate it?

[I had previously posted this question to the Math and TCS stackexchanges and didn't really pick up much traction. Someone suggested I post it here.]

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