Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Intermittency and ageing for the symbiotic branching model

Frank Aurzada and Leif Döring

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For the symbiotic branching model introduced in [Stochastic Process. Appl. 114 (2004) 127–160], it is shown that ageing and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second moments of the parabolic Anderson model with Brownian potential. Some refinements to more general (also infinite range) kernels of recent ageing results of [Ann. Inst. H. Poincaré Probab. Statist. 43 (2007) 461–480] for interacting diffusions are given.


Dans le cadre du modèle de branchement symbiotique introduit dans [Stochastic Process. Appl. 114 (2004) 127–160], nous montrons que le vieillissement et l’intermittence présentent différents comportements suivant les cas où la corrélation est négative, positive ou nulle. Notre approche permet de prouver et d’affiner de manière élémentaire des résultats classiques concernant les seconds moments du modèle parabolique d’Anderson avec potentiel Brownien. Nous raffinons aussi quelques résultats récents de vieillissement pour des diffusions interactives à noyaux généraux à portée infinie.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 2 (2011), 376-394.

First available in Project Euclid: 23 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J55: Local time and additive functionals

Ageing Interacting diffusions Intermittency Mutually catalytic branching model Parabolic Anderson model Symbiotic branching model


Aurzada, Frank; Döring, Leif. Intermittency and ageing for the symbiotic branching model. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 2, 376--394. doi:10.1214/09-AIHP356.

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