We present a new mathematical formalism for analytically obtaining the probability density function, Pn(s), of the random distance s separated by two random points distributed in a geometric object defined in n-dimensional Euclidean space. The formalism allows us to calculate Pn( s) for a spherical geometric object in n dimensions having an arbitrary non-uniform density, and reproduces the well-known results for the case of uniform density. The results find applications in elementary particle physics, statistical physics, computational science, molecular biology, geostatistics, and stochastic geometry.
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机译:我们提供了一种新的数学形式主义,用于分析性地获得随机距离 s < / italic>由分布在 n italic>维欧几里德空间中定义的几何对象中的两个随机点分隔。形式主义使我们能够为具有任意值的 n italic>尺寸的球形几何对象计算 P n sub> italic>( s italic>)密度不均匀,并在密度均匀的情况下重现众所周知的结果。这些结果可应用于基本粒子物理学,统计物理学,计算科学,分子生物学,地统计学和随机几何。
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