Rota (on page $viii$ of his introduction, page 10 of the pdf file) is talking about the difficulty of having an analytic solution for statistical mechanics in the 2-dimensional and 3-dimensional cases, while it is possible to attack the problem somewhat in the one-dimensional case.
He also mentions how stochastic methods and simulation can be used to come up with a quick-and-dirty approximation of the answers by modeling the physical sysyem and using Monte Carlo methods: iterating the system with random steps.
Topics to research would be Monte Carlo methods, stochastic models, random walks, etc. Can you say a little more about exactly what it is that you wish to study or examine?
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