随机多项式的实零点，II：对称群上的笛卡尔符号规则和反集中
Real zeroes of random polynomials, II: Descartes' rule of signs and anti-concentration on the symmetric group
摘要：
在第一部分的续集中，我们提出了一种不同的方法来界定具有实独立同分布系数或更一般地可交换系数的随机多项式的实零点的预期数量。我们表明，真正的零点的平均数不增长速度比对数的程度。我们的方法的主要成分是笛卡尔的符号规则和一个新的反浓度不等式的对称群。本文可以独立于本系列的第一部分阅读。
英文摘要：
In this sequel to Part-I, we present a different approach to bounding the expected number of real zeroes of random polynomials with real independent identically distributed coefficients or more generally, exchangeable coefficients. We show that the mean number of real zeroes does not grow faster than the logarithm of the degree. The main ingredients of our approach are Descartes' rule of signs and a new anti-concentration inequality for the symmetric group. This paper can be read independently of part-I in this series.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
