论文标题
随机弦的香肠体积和泊松陷阱中的生存
Sausage Volume of the Random String and Survival in a medium of Poisson Traps
论文作者
论文摘要
我们在泊松陷阱环境中移动聚合物的生存概率提供了渐近界。我们的聚合物模型是由添加剂时空白噪声驱动的随机热方程的矢量值解。解决方案以$ {\ mathbb r}^d，d \ geq 1 $中的值进行值。在硬质和软障碍物的情况下，我们给出上限和下限的生存概率。我们的边界衰减与$ t^{d/（d+2）} $成正比的速率衰减，这是布朗尼运动中发生的相同指数。这些指数还取决于聚合物的长度$ j $，但是在这里我们的上限和下限涉及$ j $的不同权力。 其次，我们的主要定理意味着围绕弦的维纳香肠生长的上限和下限。 Wiener香肠是以随机弦的焦点为中心的给定半径的球的结合，时间小于或等于给定值。
We provide asymptotic bounds on the survival probability of a moving polymer in an environment of Poisson traps. Our model for the polymer is the vector-valued solution of a stochastic heat equation driven by additive spacetime white noise; solutions take values in ${\mathbb R}^d, d \geq 1$. We give upper and lower bounds for the survival probability in the cases of hard and soft obstacles. Our bounds decay exponentially with rate proportional to $T^{d/(d+2)}$, the same exponent that occurs in the case of Brownian motion. The exponents also depend on the length $J$ of the polymer, but here our upper and lower bounds involve different powers of $J$. Secondly, our main theorems imply upper and lower bounds for the growth of the Wiener sausage around our string. The Wiener sausage is the union of balls of a given radius centered at points of our random string, with time less than or equal to a given value.
