Mathematical Sciences: Studies in Random Walks

首席研究员将继续他的工作， 二维和三维随机行走路径的结构。 的 感兴趣的特定对象是这些的关键指数 Walks：相交指数，用于测量 两个独立的行走相交;化学指数， 测量两点之间的最短子路径的长度; 电阻指数;循环擦除指数，用于测量 按时间顺序从擦除循环导出的路径的长度;以及 与粒子扩散行为有关的指数 随机行走路径。研究人员还将研究形成的集群 随机漫步动力学的 首席研究员将继续他的工作， 二进制和三进制随机行走路径的类分形结构 尺寸. 这是概率论的一个领域， 物理学和化学中的启发式模型 动机 这方面的结果将影响 理论物理学界和理论物理学界。 的一个目的 interest是随机游走的交集指数， 测量两个独立行走相交的概率。

The principal investigator will continue his work on the structure of random walk paths in two and three dimensions. The particular objects of interest are critical exponents for these walks: the intersection exponent, which measures the probability that two independent walks intersect; the chemical exponent, which measures the length of the shortest subpath between two points; the resistance exponent; the loop-erasing exponent, which measures the length of a path derived from erasing loop chronologically; and exponents related to the behavior of a particle diffusing on a random walk path. The investigator will also study clusters formed from random walk dynamics. The principal investigator will continue his work on the fractal-like structure of random walk paths in two and three dimensions. This is an area of probability theory that draws heavily on heuristic models in physics and chemistry for motivation. Results in this area will impact both the probability community and the theoretical physics community. One object of interest is the intersection exponent of a random walk, which measures the probability that two independent walks intersect.