Analysis of long-tailed phenomena using solvable stochastic processes

2016 Fiscal Year Final Research Report

• Project/Area Number: 25870743
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical physics/Fundamental condensed matter physics; Foundations of mathematics/Applied mathematics
• Research Institution: University of the Ryukyus (2016); Chuo University (2013-2015)
• Principal Investigator: Yamamoto Ken 琉球大学, 理学部, 講師 (00634693)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 確率過程 / ベキ分布 / 対数正規分布

Outline of Final Research Achievements

In this research project, heavy-tailed probability distributions in social and biological phenomena have been analyzed theoretically.
First, a simple stochastic model has been constructed and analyzed, which is regarded as a model for the box-office grosse of a movie. This model can explain a power-law decay in the distribution of box-office grosses. Second, we have found that the number of articles within a law follows a lognormal distribution. The tree structure whose depth is normally distributed is an appropriate model for this lognormal behavior. Third, the size distribution of bacterial cells is studied. Our analysis of a phenomenological stochastic model for the bacterial growth has given a theoretical basis for the lognormality of the cell-size distribution.

Free Research Field

数理物理学