Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps
Limiting Results for the Free Energy of Directed Polymers in Random Environment with Unbounded Jumps
复制标题
无界跳跃随机环境中定向聚合物自由能的极限结果
DOI：
10.1007/s10955-015-1347-1
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
N. Yoshida
中科院分区：
文献类型：
--
作者：
F. Comets;R. Fukushima;S. Nakajima;N. Yoshida
研究了随机环境中定向高聚物自由能的渐近性质。允许聚合物进行无界跳跃，环境由伯努利变量给出。我们首先建立了自由能的存在性和连续性，包括耦合常数的负无穷大值。我们的存在性证明与现有的证明不同之处在于它避免了直接使用次可加性.其次，我们确定了自由能在伯努利变量成功概率趋于1的极限下的渐近性。它是通过使用所谓的时间常数，一定的定向第一次通过渗流。我们的证明依赖于时间常数的某种连续性，这是独立的利益。
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. Our proof of existence atdiffers from existing ones in that it avoids the direct use of subadditivity. Secondly, we identify the asymptotics of the free energy atin 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.