Mathematical Sciences: Probabilistic Inequalities

首席研究员将对与概率论有关的各种主题进行研究，其中许多涉及概率不平等。这些主题包括预言中的最优停止和顺序选择，公平分配不等式的划分，向量度量的范围，随机性感知的第一位数含义，以及决策过程和赌博理论。这些问题在运筹学、管理科学和统计学等数学决策领域有实际应用，在经典概率论、测度论和函数论中也有理论应用。

The principal investigator will carry out research on a variety of topics related to probability theory, many involving probabilistic inequalities. These topics include optimal stopping as in prophet inequalities and order selection, partitioning of fair-division inequalities, ranges of vector measures, first-digit implications of perception of randomness, and decision processes and gambling theory. These problems have practical applications within areas of mathematical decision- making such as operations research, management science and statistics, as well as theoretical application in classical probability, measure and function theory.