Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2005-09-01
Brazilian Journal of Physics, vol. 36, no. 1B, March, 2006
Physics
Condensed Matter
Disordered Systems and Neural Networks
8 pages, 2 figures and 1 table
Scientific paper
10.1590/S0103-97332006000200017
A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to \infty$, 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 pose no major difficulty, the same is not true for large random link systems due to Euclidean restrictions. Exploring the deterministic nature of the congruential pseudo-random number generators, we present techniques which allow the consideration of models with memory consumption of order O(N), instead of $O(N^2)$ in a naive implementation but with the same time dependence $O(N^2)$.
Martinez Alexandre Souto
Sangaletti Tercariol Cesar Augusto
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