Random Polymers and De Localization Phenomena

Polymers are chemical compounds consisting essentially of repeating units, called monomers or, more properly, of monomer units. We will use indifferently monomer and monomer unit, for the precise meanings in polymer science see [Jenkins et al. (1996)]. The adverb essentially refers to the fact that in several instances the monomer units are not identical as a matter of fact this situation is rather typical, but in many cases it is not inappropriate to neglect this aspect and to model the polymer as a chain of exactly repetitive units. 

Besides this basic aspect of the heterogeneous character of the chain, real polymers are complex objects on their own, typically fluctuating in a solvent and interacting with the molecules of the solvent as well as with other portion of themselves, the so called self-interaction or excluded volume interaction (two classical references on polymers and polymer models are [Flory (1953)] and [de Gennes (1979)]). However, in simplified models, polymers are often reduced to random walk paths on a lattice and the self-interaction is modeled by the self-avoiding constraint a random walk path, self- 

added to self-avoidance, the modeling of a precise physical system requires considering the interaction of a polymer with an environment or with other polymers (with few exceptions, we will not consider this second case, see however [Fisher (1984)]) it is often the case that this extra 

While we will cite and discuss several results taken from physics, bio- 

Some recurrent notation and a (technical) suggestion In what foiiows we use the symboi with two meanings  

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