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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2018

Reaction-diffusion on the fully-connected lattice: A + A → A

Résumé

Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.
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Dates et versions

hal-01729572 , version 1 (12-03-2018)

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Loic Turban, Jean-Yves Fortin. Reaction-diffusion on the fully-connected lattice: A + A → A. Journal of Physics A: Mathematical and Theoretical, 2018, 51 (14), ⟨10.1088/1751-8121/aab0f4⟩. ⟨hal-01729572⟩
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