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

Abstract : We study asymptotic behaviors 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 the Bernoulli variables. We first establish the existence and continuity 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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https://hal.archives-ouvertes.fr/hal-01148614
Contributor : Francis Comets <>
Submitted on : Monday, May 4, 2015 - 11:41:54 PM
Last modification on : Saturday, March 28, 2020 - 2:15:44 AM

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  • HAL Id : hal-01148614, version 1
  • ARXIV : 1504.04505

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Francis Comets, Ryoki Fukushima, Shuta Nakajima, Nobuo Yoshida. Limiting results for the free energy of directed polymers in random environment with unbounded jumps. 2015. ⟨hal-01148614⟩

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