标题： 聚合物在泊松介质中的局域化转变 显示英文标题

标题： Localization Transition for Polymers in Poissonian Medium

摘要： 我们研究了在维度$1+d$中由泊松势中的布朗运动给出的随机环境中的定向聚合物模型。我们研究了非均匀性的密度和强度的影响，分别是泊松场的强度参数$\nu$和温度的倒数$\beta$。我们的结果是：(i) 相图的精细信息，包括临界曲线的定量估计；(ii) 在低温和/或高密度下的路径局部化；(iii) 在大$\nu \beta^2$和有界$\beta$的情况下在偏好走廊中的完全局部化。 显示英文摘要

摘要： We study a model of directed polymers in random environment in dimension $1+d$, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter $\nu$ of the Poisson field and the temperature inverse $\beta$. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large $\nu \beta^2$ and bounded $\beta$.