Directed Polymers in Random Environments by Francis Comets

Author:Francis Comets
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Assume for convenience that this distribution has no atoms1 and that d = 1. One can see that for any (fixed) positive finite temperature, the polymer is localized to the path along which the energy is minimal, i.e. thermal fluctuations are negligible: this is because entropy is of smaller order compared to energy in this case, and the scaling limit of the Gibbs measure reduces to that of the geodesics given in [133]. Consequently, it is natural to scale temperature β = β n with n and indeed if

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