2004/10/15 by J. M. Luck, Anita Mehta
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2005-00102-y
published as Eur. Phys. J. B 44, 79-92 (2005) · 28 pages, 8 figures
arxiv created 2004/10/15 · openalex publication_date 2005/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest' still holds in the mean-field limit, where the model exhibits glassy dynamics, with two well separated time scales, corresponding to individual and collective behaviour. The survival probability of a cluster eventually falls off according to the universal law (ln t)-1/2. Beyond mean field, the dynamics exhibits both aging and metastability, with a finite fraction of the clusters surviving forever and forming a non-trivial spatial pattern.