Stochastic urn models of innovation and search dynamics

This work is devoted to applications of the Ehrenfest urn model to innovation and search processes. In the first part we discuss systems of two urns serving as models of innovation processes. The elementary act of innovation is considered as a transition from old (technologies, way of production, behavior, decisions) to new. The survival probability of the new under the influence of stochastic effects is discussed. In the second part we study systems of s⪢1 urns serving as models for optimal solution searching in optimization problems. The problem is to find the minimum on a large set of real numbers Ui using a total of N seekers (N≃2–100) simultaneously. The potential Ui is defined on the integer set i=1,…,s, where s is extremely large. In particular, we consider the frustrated periodic strings and the merit problem. The known equations for thermodynamic search processes and for simple models of biological evolution are unified by defining a two-parameter family of equations which embeds both cases. The search parameters are controlled by means of seeker ensemble dispersion.