Plaquette Percolation

概率论与许多其他领域，如组合学和遍历论之间的相互作用有着漫长而富有成果的历史。这一建议将在随机简单复合体、随机矩阵理论、极值组合学和几何群论等领域进一步深化这些联系。本文特别关注以下领域的问题：随机简单复体的拓扑结构、随机矩阵的谱、高维渗透的推广和有限型的子移。从相互矛盾的政治民意调查到股市波动，随机性在现代生活的许多方面都很明显。概率论是试图量化随机性的数学分支。在过去的几十年里，概率论的语言、思想和结果已经应用于许多不同的数学分支。本提案旨在延续这一趋势，并扩展概率论与几个数学分支之间的联系。这个建议也将概率论应用于拓扑学，这是数学的一个分支，直到最近才与概率论有很少的互动。该基金将赞助讲座，让本科生了解数学在各个领域的应用方式。

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.