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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 2: Dynamics of Social and Financial Networks

SOE 2.2: Topical Talk

Monday, March 31, 2014, 10:30–11:00, GÖR 226

Statistical Mechanics of a Firm Growth Process — •Cornelia Metzig — Université Joseph Fourier, Grenoble, France

A stochastic process for firm growth is analyzed, which arises from competition for a scarce quantity. In its nonequilibrium stationary state, the model exhibits a tent-shaped growth rate distribution, a heavy tailed size distribution, and a growth rate variance which scales as a power of firm size. These results reproduce qualitatively three stylized facts found in firm databases. Market allocations of the quantity – like workforce or purchasing power of customers – happens such that every market realization has the same probability. Firms demand a quantity proportional to their actual size n, and the number of actually received resources is binomially distributed, with n dependent variance. Fluctuations of this process are described by the linear Langevin equation for the size n. A well-known case is a system with additive fluctuations, as in equilibrium systems, leading to a Gaussian stationary distribution, and multiplicative fluctuations, where the stationary distribution exhibits a power law tail. In the latter, superstatistics can be used, which can be seen as a way of mapping multiplicative noise onto n-dependent additive noise. In contrast, in this model, fluctuations are neither simply additive nor multiplicative, since the fluctuations scale as a power ≠ 1 of n. Despite this difference, the concept of superstatistics can be applied to explain the aggregate growth rate distribution. Here, it consists of expressing the fluctuations as n-dependent multiplicative noise, and then integrate over all sizes. Theoretical an numerical results for firms’ size and firms’ growth rate distribution are given.