Intermittency and ageing for the symbiotic branching model
Résumé
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. Poincare Probab. Statist. 43 (2007) 461-480] for interacting diffusions are given.