We consider the population dynamics that are implemented by the cloning algorithmfor analysis of large deviations of time-averaged quantities. We consider exclusionprocesses acting on particles on one-dimensional lattices such as the simple symmetricexclusion process and the Fredkin Process. We use large deviation theoryto quantify the probabilities of rare events. To achieve this we adapt a numericalalgorithm which employs a combination of biased cloning and simulation of modi-ed dynamics. We establish its accuracy within particular regimes, determine whichcongurations are likely to produce rare events and quantify the convergence of thealgorithm with respect to algorithmic parameters. We investigate the eciency andspeed-up obtained when using dierent parallelisation techniques to implement thealgorithm which involves complex communication patterns between systems.
|Date of Award||1 May 2019|
|Supervisor||Stephen Clark (Supervisor), Robert Jack (Supervisor) & Russell Bradford (Supervisor)|