期望欧拉示性数启发式的有效性
Validity of the expected Euler characteristic heuristic
摘要：
研究了光滑、中心化、单位方差高斯过程f的最大值分布的期望欧拉示性数逼近的精度。使用一个点过程表示的错误，有效的任意光滑过程，我们表明，误差一般是指数小于任何项的近似。我们也给出了这个指数衰减率的一个下界，它是由原始过程f导出的高斯过程族f^x的最大方差。
英文摘要：
We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f^x, derived from the original process f.
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。
