A random walk inside the simplex: unemployment and MINIMAC

Random walk in labor supply space. The dimensions would be employment at different firms or in different industries.

As part of my outline of paper #2, I put together a couple of posts that create an interesting result. I previously built a version of MINIMAC (mini macro model) as described by Paul Krugman here as an information equilibrium/maximum entropy model. One consequence of that model is that you can derive a natural rate of unemployment fairly simply.
If we treat the problem as a random walk inside the simplex (bounded by the labor supply, pictured at the top), we get a simple model of spikes in the unemployment rate (shown for a d = 40 dimensional simplex):

Occasional spikes in unemployment, that are caused by randomly moving through the employment state space.
This is to say that you could get spikes in unemployment for no reason whatsoever ... it's just randomly moving around the employment state space. I think I'd still lean towards this model, however.