Journal title
Journal of Statistical Mechanics: Theory and Experiment
DOI
10.1088/1742-5468/aab50a
Issue
4
Volume
2018
Last updated
2023-10-02T19:36:35.983+01:00
Abstract
We consider a simple model of firm/city/etc growth based on a multi-item criterion: whenever entity B fares better than entity A on a subset of M items out of K, the agent originally in A moves to B. We solve the model analytically in the cases K = 1 and . The resulting stationary distribution of sizes is generically a Zipf-law provided M > K/2. When , no selection occurs and the size distribution remains thin-tailed. In the special case M = K, one needs to regularize the problem by introducing a small 'default' probability phgr. We find that the stationary distribution has a power-law tail that becomes a Zipf-law when . The approach to the stationary state can also be characterized, with strong similarities with a simple 'aging' model considered by Barrat and Mézard.
Symplectic ID
1145383
Submitted to ORA
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Publication type
Journal Article
Publication date
09 Apr 2018