Two-species diffusion-annihilation process on the fully-connected lattice: probability distributions and extreme value statistics - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2018

Two-species diffusion-annihilation process on the fully-connected lattice: probability distributions and extreme value statistics

Loic Turban

Résumé

We study the two-species diffusion-annihilation process, A + B → Ø, on the fully-connected lattice. Probability distributions for the number of particles and the reaction time are obtained for a finite-size system using a master equation approach. Mean values and variances are deduced from generating functions. When the reaction is far from complete, i.e. for a large number of particles of each species, mean-field theory is exact and the fluctuations are Gaussian. In the scaling limit the reaction time displays extreme-value statistics in the vicinity of the absorbing states. A generalized Gumbel distribution is obtained for unequal initial densities, ρ A > ρ B. For equal or almost equal initial densities, ρ A ≃ ρ B , the fluctuations of the reaction time near the absorbing state are governed by a probability density involving derivatives of ϑ 4 , the Jacobi theta function.
Fichier principal
Vignette du fichier
1802.09440.pdf (676.78 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01833987 , version 1 (10-07-2018)

Identifiants

Citer

Loic Turban. Two-species diffusion-annihilation process on the fully-connected lattice: probability distributions and extreme value statistics. Journal of Physics A: Mathematical and Theoretical, 2018, 51 (32), ⟨10.1088/1751-8121/aaccc1⟩. ⟨hal-01833987⟩
35 Consultations
48 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More