Greedy algorithms and Zipf laws
| Autor: | Jean-Philippe Bouchaud, José Moran |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
0301 basic medicine
Statistics and Probability Stationary distribution Statistical Mechanics (cond-mat.stat-mech) Zipf's law Selection (relational algebra) Distribution (number theory) 05 social sciences FOS: Physical sciences Statistical and Nonlinear Physics FOS: Economics and business Combinatorics 03 medical and health sciences 030104 developmental biology Simple (abstract algebra) 0502 economics and business 050207 economics Statistics Probability and Uncertainty Special case General Finance (q-fin.GN) Greedy algorithm Quantitative Finance - General Finance Stationary state Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that 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 $K \to \infty$. The resulting stationary distribution of sizes is generically a Zipf-law provided $M > K/2$. When $M \leq K/2$, no selection occurs and the size distribution remains thin-tailed. In the special case $M=K$, one needs to regularise the problem by introducing a small "default" probability $��$. We find that the stationary distribution has a power-law tail that becomes a Zipf-law when $��\to 0$. The approach to the stationary state can also been characterized, with strong similarities with a simple "aging" model considered by Barrat & M��zard. |
| Databáze: | OpenAIRE |
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