Length distribution of fuzzy-end segments

We have calculated and discussed the probability density distributions of lengths of fuzzy-end segments, i. e. segments the ends of which assume random positions. We per-formed our calculations for several simple cases in 1, 2 and 3 dimensions: one end fixed, the other assuming a random position, and both ends at random positions. The obtained statistical data may serve as reference data for calculations of stochastic-geometrical properties of complex systems, such as conformations of complicated bolted construc-tions with clearances (in structure mechanics) or energy transfer processes between molecules in diluted systems (in physics).