The symbiotic branching model is a spatial population model describing the dynamics of two interacting types that can only branch if both types are present. A classical result for the underlying stochastic partial differential equation identifies moments of the solution via a duality to a system of Brownian motions with dynamically changing colors. In this paper, we revisit this duality and give it a new interpretation. This new approach allows us to extend the duality to the limit as the branching rate γ is sent to infinity. This limit is particularly interesting since it captures the large scale behavior of the system. As an application of the duality, we can explicitly identify the γ = ∞ limit when the driving noises are perfectly negatively correlated. The limit is a system of annihilating Brownian motions with a drift that depends on the initial imbalance between the types.
- Annihilating Brownian motions
- Moment duality
- Mutually catalytic branching
- Rescaled interface
- Stepping stone model
- Symbiotic branching model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
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- Department of Mathematical Sciences - Senior Lecturer
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath
Person: Research & Teaching