REU SITE: Mathematical Sciences: Discrete Random Structures

项目摘要离散随机结构这个为期五年的项目“离散随机结构”将使首席研究员能够进一步巩固他对本科研究的深入参与。 他将带领八名学生，每年在一系列有意义的数学研究工作，每一个旨在说服参与者，有几个子学科之间不可否认的联系，这些债券需要得到承认和利用。 团队成员的问题将在组合学，数论，几何，算法和分子生物学等领域产生，但当代概率方法和经典分析技术将被用作解决问题的整体工具。 我们预计，大多数与会者将研究最近开发的概率技术，如詹森不等式;方法的有界和无界鞅差;塔拉格兰德的等周不等式;和斯坦陈方法的泊松近似在他们的努力，以了解浓度的措施，范围广泛的离散结构。 参加者将在全国范围内搜索后选出，并将于1997年至2001年夏季在密歇根理工大学度过两个月。根据PI在过去七年的记录，可以预测学生 研究人员将单独或以两人或两人以上的小组平均研究三个问题，并能够在其中两个问题上取得重大进展。 学生们的研究结果将在国家会议上发表，如年度AMS/MAA会议，或在精心挑选的概率/组合学会议上。 与过去一样，将尽一切努力将学生的论文提交给高水平期刊，以便发表。 我们将从广泛的学院和大学中选拔学生，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.