We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.

中文翻译：

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随机带限函数节点域的体积分布

我们研究了一般流形上自然产生的高斯随机场族的节点域的体积分布，即随机带限函数。发现在高能量极限下，典型实例服从确定性普遍规律，与流形无关。建立了该定律的一些基本定性性质，如累积概率函数的支持性、单调性和连续性。