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When you say "large space of possibilities" do you mean when you have a large number of parameters to estimate? The basic issue there is that probability densities get weird in high dimensions: specifically the density becomes too spread out and a sampler has a hard time coping. Michael Betancourt has a nice introduction to Hamiltonian MCMC that also deals conceptually with some of the problems with MCMC in high-dim settings in the first few sections. If you want more specifics you might also look at general discussions of probability in high dimensions, although you'll need to think about how this intersects with the behavior of an MCMC sampler.