General formulas are presented for higher order cumulants of the conserved charge statistical fluctuations inside the mixed phase. As a particular example, the van der Waals model in the grand canonical ensemble is used. The higher order measures of the conserved charge fluctuations up to the hyperkurtosis are calculated in a vicinity of the critical point (CP). The analysis includes both the mixed phase region and the pure phases on the phase diagram. It is shown that even-order fluctuation measures, e.g., scaled variance, kurtosis, and hyperkurtosis, have only positive values in the mixed phase and go to infinity at the CP. For odd-order measures, such as skewness and hyperskewness, the regions of positive and negative values are found near the left and right binodals, respectively. The obtained results are discussed in a context of the event-by-event fluctuation measurements in heavy-ion collisions.

中文翻译：

---

混合相内部的高阶守恒电荷波动

给出了混合相内部守恒电荷统计波动的高阶累积量的通用公式。作为一个特定示例，使用了大正则合奏中的范德华斯模型。在临界点（CP）附近，计算出直至超峰度为止的守恒电荷波动的高阶测量。分析包括相图上的混合相区域和纯相。结果表明，偶数级波动量度（例如，标度方差，峰度和峰度）在混合相中仅具有正值，并且在CP处变为无穷大。对于偏度和偏度等奇数量度，分别在左侧和右侧底角附近找到正值和负值区域。