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May 30, 2013 at 17:29 comment added fedja Nope. The stationary measure us trivial: the uniform distribution on all configurations. What I mean is that I have no idea how to find what they call $\sigma^2$ with any decent precision for this huge chain in terms of $k$ and $d$.
May 30, 2013 at 11:15 comment added R W Don't see any problem here. Look at Pre-theorem 2.1 from the paper I quote, condition (iii). The only difficulty might be in finding the stationary measure - is this what you mean?
May 30, 2013 at 2:35 comment added fedja Yes, of course. However, the devil here is in the computation of correlations between steps. Even the asymptotic regime doesn't look trivial to me :(.
May 29, 2013 at 13:10 history answered R W CC BY-SA 3.0