标题： 自斥星形聚合物的半径 显示英文标题

标题： The radius of a self-repelling star polymer

摘要： 我们研究一维、二维和三维中弱自避星形聚合物的有效半径。 我们的模型包括从原点出发，到时间$T$的$N$个布朗运动，并受到基于它们彼此之间或自身附近停留时间的指数惩罚。 有效半径衡量的是从原点的典型距离。 我们的主要结果给出了有效半径的估计，在二维和三维中我们施加了$T \leq N$的限制。 我们结果的一个亮点是，在二维情况下，我们发现半径与$T^{3/4}$成正比，仅存在对数修正。 我们的结果可能有助于理解一个著名的猜想，即对于二维中的单个自避随机游走，到时间$T$的端到端距离大致为$T^{3/4}$。 显示英文摘要

摘要： We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes $N$ Brownian motions up to time $T$, started at the origin and subject to exponential penalization based on the amount of time they spend close to each other, or close to themselves. The effective radius measures the typical distance from the origin. Our main result gives estimates for the effective radius where in two and three dimensions we impose the restriction that $T \leq N$. One of the highlights of our results is that in two dimensions, we find that the radius is proportional to $T^{3/4}$, up to logarithmic corrections. Our result may shed light on the well-known conjecture that for a single self-avoiding random walk in two dimensions, the end-to-end distance up to time $T$ is roughly $T^{3/4}$.