随机串的香肠体积与Poisson陷阱中的生存
Sausage Volume of the Random String and Survival in a medium of Poisson Traps
摘要：
我们提供了一个移动的聚合物在泊松陷阱的环境中的生存概率的渐近界。我们的聚合物模型是由加性时空白噪声驱动的随机热方程的向量值解;解取${\mathbb R}^d, d \geq 1$中的值。我们给出了硬障碍和软障碍情况下生存概率的上界和下界。我们的边界以与$T^{d/(d+2)}$成比例的速率呈指数衰减，与布朗运动的情况下发生的指数相同。指数还取决于聚合物的长度$J$，但这里我们的上限和下界涉及$J$的不同幂。其次，我们的主要定理暗示了我们弦周围维纳香肠增长的上界和下界。维纳香肠是以我们的随机串的点为中心的给定半径的球的并集，时间小于或等于给定值。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
