On the Return Time Viewpoint

It is by now clear that the models that we are considering may be reduced, completely or partially, to return time models, when they are not defined from the start simply via return times in particular, there is no loss of 

Let us write explicitly the general return time model this will be useful in Chapter 4, where we are going to prove the existence of the free energy, but also on a conceptual level, since it suggests a general abstract class of models to which the techniques we develop may be applied. In what follows the reader should keep in mind in particular formulas (1.63) and (1.64). 

For every typical realization of a renewal process t we introduce the general Hamiltonian 

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