Entropic Repulsion and Wetting Phenomena

Important and often challenging questions arise in the analysis of interfaces between different phases or different materials, possibly connected to the presence of geometrical constraints like the presence of an impenetrable region. The statistical mechanics modeling of interfaces often resorts to the so called reduced models, that is to models in which the complexity is reduced by imposing to the trajectories of the process to be functions. In two dimensions, this naturally leads to random walk based models, see Appendix C.l. 

In order to understand a bit better this repulsion effect let us consider the model (1.29) with / = 0. In Section 2.2 we are going to show that N fi for a suitable c 0 (the precise value 3/2 of the 

The situation for / is really different. This time, as we have already seen (c/. (1.10)), by the classical Renewal Theorem (Theorem A.3) 

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