Power-law tails in nonstationary stochastic processes with asymmetrically multiplicative interactions
| dc.creator | Fujihara, Akihiro | |
| dc.creator | Ohtsuki, Toshiya | |
| dc.creator | Yamamoto, Hiroshi | |
| dc.date | 2005-06-30 | |
| dc.date.accessioned | 2026-07-07T03:05:51Z | |
| dc.date.available | 2026-07-07T03:05:51Z | |
| dc.description | We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge y), where (0 \le) a, b (\le 1) and c, d (> 0) are interaction parameters. Noninteger power-law tails in the probability distribution function of scaled quantities are analyzed in a similar way as in inelastic Maxwell models. A transcendental equation to determine the growth rate γof the processes and the exponent s of the tails is derived formally from moment equations in Fourier space. In the case c=d or a+b=1 (a \neq 0, 1), the first-order moment equation admits a closed form solution and γand s are calculated analytically from the transcendental equation. It becomes evident that at c=d, exchange rate b of small quantities is irrelevant to power-law tails. In the case c \neq d and a+b \neq 1, a closed form solution of the first-order moment equation cannot be obtained because of asymmetry of interactions. However, the moment equation for a singular term formally forms a closed solution and possibility for the presence of power-law tails is shown. Continuity of the exponent s with respect to parameters a, b, c, d is discussed. Then numerical simulations are carried out and campared with the theory. Good agreement is achieved for both γand s. | |
| dc.description | 9 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0506785 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0506785 | |
| dc.identifier | PHYSICAL REVIEW E 70, 031106 (2004) | |
| dc.identifier | doi:10.1103/PhysRevE.70.031106 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/26600 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Power-law tails in nonstationary stochastic processes with asymmetrically multiplicative interactions | |
| dc.type | text |