Limiting results for the free energy of directed polymers in random environment with unbounded jumps

F. Comets 1 R. Fukushima S. Nakajima N. Yoshida
1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
Abstract : We study asymptotics of the free energy for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by Bernoulli variables. We first establish the existence and continuity of the free energy including the negative infinity value of the coupling constant β. Our proof of existence at β=−∞ differs from existing ones in that it avoids the direct use of subadditivity. Secondly, we identify the asymptotics of the free energy at β=−∞ in the limit of the success probability of the Bernoulli variables tending to one. It is described by using the so-called time constant of a certain directed first passage percolation. Our proof relies on a certain continuity property of the time constant, which is of independent interest.
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Article dans une revue
Journal of Statistical Physics, Springer Verlag, 2015, 161 (3), pp.577-597. <10.1007/s10955-015-1347-1>
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Contributeur : Serena Benassù <>
Soumis le : jeudi 28 janvier 2016 - 11:41:51
Dernière modification le : jeudi 27 avril 2017 - 09:46:51

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F. Comets, R. Fukushima, S. Nakajima, N. Yoshida. Limiting results for the free energy of directed polymers in random environment with unbounded jumps. Journal of Statistical Physics, Springer Verlag, 2015, 161 (3), pp.577-597. <10.1007/s10955-015-1347-1>. <hal-01263805>

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