Hydrodynamic limit for the $A+Bto emptyset$ model
- Bovier, Anton
- Černý, Jiri
2010 Mathematics Subject Classification
- 82D30 82C41 60F17
- hydrodynamic limit, large deviations, order book dynamics
We study a two-species interacting particle model on a subset of $Z$ with open boundaries. The two species are injected with time dependent rate on the left, resp. right boundary. Particles of different species annihilate when they try to occupy the same site. This model has been proposed as a simple model for the dynamics of an ``order book'' on a stock market. We consider the hydrodynamic scaling limit for the empirical process and prove a large deviation principle that implies convergence to the solution of a non-linear parabolic equation.