An efficient algorithm to generate random uncorrelated Euclidean distances: the random link model - Terçariol,César Augusto Sangaletti (2006)
A disordered medium is often constructed by N random points independently and identically distributed in a d-dimensional hyperspace. Characteristics related to the statistics of this system are known as the random point problem. As d ® ¥, the distances between two points become independent random variables, leading to its mean field description: the random link model. While the numerical treatment of large random point problems poses no major difficulty, due to Euclidean restrictions the same is not true for large random link systems. Exploring the deterministic nature of the pseudo-random number generators, we present techniques which allow to consider models with memory consumption of O(N), instead of O(N²) obtained by a naive implementation, but with the same time dependence O(N²).