Plaquette Percolation

概率论与组合数学、遍历理论等许多领域之间的相互作用有着悠久而富有成果的历史。这一建议将进一步许多这些连接在一些领域，包括随机单纯复形随机矩阵理论，极值组合学和几何群论。特别是这个建议集中在以下领域的问题：拓扑结构的随机单纯复形，频谱的随机矩阵，高维广义的渗流和subshifts的有限type.Randomness是显而易见的，在许多方面的现代生活中，从冲突的政治民意调查的波动在股票市场。概率论是数学的一个分支，它试图量化随机性。在过去的几十年里，概率论的语言、思想和结果已经被应用于数学的许多不同分支。这一提议试图延续这一趋势，并扩展概率论与数学的几个分支之间的联系。该提案还将概率论应用于拓扑学，拓扑学是数学的一个分支，直到最近与概率几乎没有相互作用。这笔赠款将赞助讲座，让本科生了解数学应用于各个领域的方式。

There is a long and fruitful history of interaction between probability and many other fields such as combinatorics and ergodic theory. This proposal will further many of these connections in a number of fields including random simplicial complexes random matrix theory, extremal combinatorics and geometric group theory. In particular this proposal focuses on problems in the following areas: topology of random simplicial complexes, spectrum of random matrices, higher dimensional generalizations of percolation and subshifts of finite type.Randomness is evident in many aspects of modern life from conflicting political polls to fluctuations in the stock market. Probability theory is the branch of mathematics which tries to quantify randomness. Over the last few decades the language, ideas and results from probability theory have been applied to many different branches of mathematics. This proposal seeks to continue this trend and extend the connections between probability theory and several branches of mathematics. This proposal also will apply probability theory to topology, a branch of mathematics which until recently has had little interaction with probability. The grant has will sponsor talks that will let undergraduates learn about the ways that mathematics has been applied to a variety of fields.