The Ehrenfest Fleas: From Model to Theory

Authors: Costantini D.¹; Garibaldi U.²

Source: Synthese, Volume 139, Number 1, March 2004 , pp. 107-142(36)

Publisher: Springer

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Abstract:

A generalization of Ehrenfest's urn model is suggested. This will allow us to treat a wide class of stochastic processes describing the changes of microscopic objects. These processes are homogeneous Markov chains. The generalization proposed is presented as an abstract conditional (relative) probability theory. The probability axioms of such a theory and some simple additional conditions, yield both transition probabilities and equilibrium distributions. The resulting theory interpreted in terms of particles and single-particle states, leads to the usual formulae of quantum and classical statistical mechanics; in terms of chromosomes and allelic types, it allows the deduction of many genetical models including the Ewens sampling formula; in terms of agents' strategies, it gives a justification of the ``herd behaviour'' typical of a population of heterogeneous economic agents.

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:SYNT.0000021307.64103.b8

Affiliations: 1: Clinical Epidemiology National Cancer Research Institute Genova Italy 2: Dip. Fisica via Dodecaneso 33, 16146 Genova Italy, Email: garibaldi@fisica.unige.it

Publication date: 2004-03-01