On the principle of minimum growth rate in multiplicatively interacting stochastic processes

Details On the principle of minimum growth rate in multiplicatively interacting stochastic processes On the principle of minimum growth rate in multiplicatively interacting stochastic processes

2006-08-08

arxiv.org/abs/cond-mat/0608205v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

A method of moment inequalities is used to derive the principle of minimum growth rate in multiplicatively interacting stochastic processes(MISPs). When a value of a power-law exponent at the tail of probability distribution function exists in a range $0 < s \le 1$, a first-order moment diverges and an equality for a growth rate of systems breaks down. From the estimate of inequalities, we newly find a conditional inequality which determines the growth rate, and then the exponent in $0 < s \le 1$.

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