Mathematical Sciences: Isoperimetric Inequalities and LowerBounds for Stochastic Processes

数学科学：随机过程的等周不等式和下界

• 批准号: 9101452
• 负责人: Michel Talagrand
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1995-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101452&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Isoperimetric; Inequalities; LowerBounds

Professor Talagrand's research will be in three main areas. He will study lower bounds for Bernoulli processes with a view to proving a conjecture involving a norm incorporating the geometry of two Banach spaces. He will continue his research in isoperimetric inequalities. He will study the notion of type and cotype in Banach spaces. This research is at the interface of two fields: probability theory and the geometry of infinite dimensional spaces (Banach spaces). Probabilistic ideas are useful in understanding Banach spaces and conversely the quest to understand these spaces leads to new and interesting questions in pure probability.

塔拉格兰德教授的研究将集中在三个主要领域。他将研究伯努利过程的下界，以证明一个包含两个巴拿赫空间几何的范数的猜想。他将继续研究等周不等式。他将研究巴拿赫空间中的类型和共类型的概念。本研究是两个领域的交叉：概率论和无限维空间（巴拿赫空间）的几何。概率思想对理解巴拿赫空间很有用，反过来，理解这些空间的探索会导致纯概率中新的和有趣的问题。