Mathematical Sciences: Topics in Probability Theory: Statistical Mechanics Type Models and Sums of Independent Random Variables

要研究概率论中的几个问题。前三个模型与统计物理密切相关，而最后一个模型处理的是更传统的独立、同分布随机变量的和。具体问题包括寻找随机增长模型的半径边界，研究随机电阻网络的一些性质，以及研究第一通道和最后通道渗透的渐近形状。本研究将探讨一些受统计物理学启发的概率模型。这些包括渗流理论中的关键现象，扩散限制聚集和第一通道渗流。此外，研究者还将研究独立的同分布随机变量的和的散度标准，其中一些大的和已被删除。

Several problems in probability theory are to be studied. The first three concern models which are closely related to statistical physics, while the last one deals with the more traditional topic of sums of independent, identically distributed random variables. Particular problems include finding bounds on the radius of a stochastic growth model, investigating some properties of random resistor networks, and studying the asymptotic shape of first and last passage percolation. This research will investigate some probabilistic models inspired by statistical physics. These include critical phenomena in percolation theory, diffusion limited aggregation , and first-passage percolation. In addition, the investigator will also look at criteria for divergence of sums of independent, identically distributed random variables from which some large summands have been removed.