Universal features of information spreading efficiency on $d$-dimensional lattices

TL;DR

This paper extends a model of information spreading to d-dimensional lattices, revealing how lattice structure influences spreading time and showing mean-field theory's accuracy for dimensions greater than two.

Contribution

It introduces a generalized model for information spread on d-dimensional lattices, analyzing the effects of dimensionality and geometry on spreading efficiency.

Findings

Mean-field theory is exact for dimensions greater than two.

Lattice structure significantly impacts spreading time.

Final information degree exhibits nonmonotonic behavior independent of geometry.

Abstract

A model for information spreading in a population of $N$ mobile agents is extended to $d$-dimensional regular lattices. This model, already studied on two-dimensional lattices, also takes into account the degeneration of information as it passes from one agent to the other. Here, we find that the structure of the underlying lattice strongly affects the time $\tau$ at which the whole population has been reached by information. By comparing numerical simulations with mean-field calculations, we show that dimension $d=2$ is marginal for this problem and mean-field calculations become exact for $d > 2$. Nevertheless, the striking nonmonotonic behavior exhibited by the final degree of information with respect to $N$ and the lattice size $L$ appears to be geometry independent.