Log-normal distribution in growing systems with weighted multiplicative interactions
| dc.creator | Fujihara, Akihiro | |
| dc.creator | Tanimoto, Satoshi | |
| dc.creator | Ohtsuki, Toshiya | |
| dc.creator | Yamamoto, Hiroshi | |
| dc.date | 2005-11-25 | |
| dc.date | 2006-05-10 | |
| dc.date.accessioned | 2026-07-07T06:49:24Z | |
| dc.date.available | 2026-07-07T06:49:24Z | |
| dc.description | Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities $x, y$ is controlled by a homogeneous symmetric kernel $K(x, y) \propto x^{w} y^{w}$ with a weight parameter $w$. When $w<0$, a method of moment inequalities is used to derive log-normal type tails in probability distribution functions. The variance of log-normal distributions is expressed in terms of the weight $w$ and interaction parameters. When interactions are weak and a growth rate of systems is small, in particular, the variance is in proportion to the growth rate. This behavior is totally different from that of one-body stochastic processes, where the variance is independent of the growth rate. At $w>0$, Monte Carlo simulations show that the processes end up with a winner-take-all state. | |
| dc.description | 4 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0511625 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0511625 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104331 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Log-normal distribution in growing systems with weighted multiplicative interactions | |
| dc.type | text |