Abstract
The continuousspace symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions, the interface where both populations coexist remains compact. Together with a diffusive scaling property, this suggests the presence of an interesting scaling limit. Indeed, in the present paper, we show weak convergence of the diffusively rescaled populations as measurevalued processes in the Skorokhod, respectively the Meyer–Zheng, topology (for suitable parameter ranges). The limit can be characterized as the unique solution to a martingale problem and satisfies a “separation of types” property. This provides an important step toward an understanding of the scaling limit for the interface. As a corollary, we obtain an estimate on the moments of the width of an approximate interface.
Original language  English 

Pages (fromto)  807866 
Number of pages  60 
Journal  Annals of Probability 
Volume  44 
Issue number  2 
Early online date  14 Mar 2016 
DOIs  
Publication status  Published  31 Mar 2016 
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Marcel Ortgiese
 Department of Mathematical Sciences  Senior Lecturer
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Probability Laboratory at Bath
Person: Research & Teaching