高斯随机SU（m+1）多项式空穴概率的衰减阶
The order of the decay of the hole probability for Gaussian random SU(m+1) polynomials
摘要：
我们证明了对于一个大次数N的高斯随机SU（m+1）多项式，在半径为r的圆盘中没有零点的概率小于$e^{-c_{1,r} N^{m+1}}$，也大于$e^{-c_{2,r} N^{m+1}}$ .在此结果的途中，我们还得到一个更一般的结果：概率估计的事件的体积的零集的随机高次多项式偏离其平均值显着。
英文摘要：
We show that for Gaussian random SU(m+1) polynomials of a large degree N the probability that there are no zeros in the disk of radius r is less than $e^{-c_{1,r} N^{m+1}}$, and is also greater than $e^{-c_{2,r} N^{m+1}}$. Enroute to this result, we also derive a more general result: probability estimates for the event where the volume of the zero set of a random polynomial of high degree deviates significantly from its mean.
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。
