REU SITE: Mathematical Sciences: Discrete Random Structures

项目摘要离散随机结构为期五年的项目“离散随机结构”将使首席研究人员能够进一步巩固他对本科生研究的深度参与。他每年将带领8名学生进行一系列有意义的数学研究工作，每项工作都旨在让参与者相信，几个子学科之间存在着不可否认的联系，这些联系需要得到承认和利用。团队成员的问题将产生在组合学、数论、几何、算法和分子生物学等领域，但当代概率方法和经典分析技术将作为解决方案的完整工具。我们预计，大多数参与者将学习最近发展起来的概率技术，如Janson不等式、有界和无界鞅差方法、TALAGRAND等周不等式和Poisson近似的Stein-Chen方法，以努力理解大范围离散结构的集中度。参与者将在全国范围内寻找后选出，并将于1997-2001年的夏天在密歇根理工大学度过两个月。根据PI在过去七年中的记录，可以预测，学生研究人员平均将单独或以两人或两人以上的小组研究三个问题，并能够在其中两个方面取得重大进展。学生们的发现将在国家会议上公布，例如年度AMS/MAA会议，或在精心挑选的概率/组合会议上。与以往一样，我们将尽一切努力将学生的论文提交给高水平的期刊，以便有可能发表。我们将从广泛的学院和大学中挑选学生，并完全致力于大力招收妇女、少数民族和残疾学生。

Project Abstract Discrete Random Structures The five-year project "Discrete Random Structures" will enable the Principal Investigator to further consolidate his deep involvement with undergraduate research. He will lead eight students each year in a series of meaningful mathematical research endeavours, each designed to convince the participants that there are undeniable links between several sub-disciplines, and that these bonds need to be recognized and exploited. The team-members' problems will emanate in areas such as combinatorics, number theory, geometry, algorithms, and molecular biology, but contemporary probabilistic methods and classical analytic techniques will be used as integral tools in their solution. We expect that most participants will study recently developed probabilistic techniques such as Janson's inequality; the method of bounded and unbounded martingale differences; Talagrand's isoperimetric inequalities; and the Stein-Chen method of Poisson approximation in their effort to understand the concentration in measure of a wide range of discrete structures. The participants will be selected after a nationwide search, and will spend two months at Michigan Tech University during the Summers of 1997--2001. Based on the PI's track record over the last seven years, it can be predicted that the student researchers will work on an average of three problems, either individually or in teams of two or more, and be able to make significant progress on about two of these endeavours. The students' findings will be presented at national meetings such as the Annual AMS/MAA Meeting, or at a carefully selected Probability/Combinatorics conference. As in the past, every effort will be made to submit the students' papers to high-level journals for possible publication. We shall select students from a broad range of colleges and universities, and are totally committed to the vigorous recruitment of women, minorities and disabled students.