Journal
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
Volume 87, Issue 3, Pages -Publisher
PHYSICAL SOC JAPAN
DOI: 10.7566/JPSJ.87.034001
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A growing system with weighted and multiplicatively interacting particles is investigated. Each particle has a quantity that changes multiplicatively after a binary interaction, with its growth rate controlled by a weight parameter in a homogeneous symmetric kernel. We consider the system using moment inequalities and analytically derive the log-normal-type tail in the probability distribution function of quantities when the parameter is negative, which is different from the result for single-body multiplicative processes. We also find that the system approaches a winner-take-all state when the parameter is positive.
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