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Solution of a one-dimensional stochastic model with branching and coagulation reactions

Mauro Mobilia·Pierre-Antoine Bares
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Abstract

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.

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Mauro Mobilia, Pierre-Antoine Bares. 2001-09-27. Solution of a one-dimensional stochastic model with branching and coagulation reactions. https://doi.org/10.1103/physreve.64.045101

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