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11
votes
Do Random Walks on the Hexagonal Lattice have a limit?
If you want to derive the Functional CLT for this process from Donsker's theorem, you have to add a couple of small ingredients.
Donsker's applies to random walks with i.i.d. steps. Yours is not qui …
5
votes
The metric of the expected difference of random variables
I have not seen concretely your metric, but something similar is used to analyze extrema of Gaussian random fields. A very useful notion is entropy with respect to the following metric: $d(s,t)=(\math …