Herding and clustering: Ewens vs. Simon–Yule models |
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| Institution: | 1. LABORatorio Riccardo Revelli, via Real Collegio 30, 10024 Moncalieri (Turin), Italy;2. INFN, University of Genoa, Department of Physics, via Dodecaneso 33, 16146 Genoa, Italy;3. IMEM-CNR, University of Genoa, c/o Department of Physics, via Dodecaneso 33, 16146 Genoa, Italy;4. National Cancer Research Institute (IST), Largo Benzi 10, Genoa 16132, Italy;1. Université del Piemonte Orientale, Dipartimento de Scienze e Tecnologie Avanzate, Via Bellini 25 G, 15100 Alessandria AL, Italy;1. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706, USA;2. Mathematische Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany;1. Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy;2. Nano-Bio Spectroscopy Group, Departamento de Fìsica de Materiales, Universidad del Paìs Vasco UPV/EHU, E-20018 San Sebastiàn, Spain;1. Department of Mathematics, Uppsala University, 751 06, Uppsala, Sweden;2. Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 412 96 Gothenburg, Sweden;1. Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain;2. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, Granada, Spain;3. Departamento de Matemática Aplicada, E.T.S. Ingenieros Industriales, Universidad Politécnica de Madrid, Madrid, Spain;4. Instituto “Carlos I” de Física Teórica y Computacional, Universidad de Granada, Granada, Spain |
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| Abstract: | Clustering has often described by Ewens Sampling Formula (ESF). Focusing the attention on the evergreen problem of the size of firms, we discuss the compatibility of empirical data and ESF. In order to obtain a power law for all sizes in the present paper we shall explore the route inspired by Yule, Zipf and Simon. It differs from the Ewens model both for destruction and creation. In particular the probability of herding is independent on the size of the herd. Computer simulations seem to confirm that actually the mean number of clusters of size i (the equilibrium distribution) follows the corresponding Yule distribution. Finally we introduce a finite Markov chain, that resembles the marginal dynamics of a cluster, which drives the cluster to a censored Yule distribution. |
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