Adaptive power method for estimating large deviations of Markov chains

I will discuss a stochastic algorithm based on a power method that adaptively learns the large deviation functions characterising the fluctuations of additive functionals of Markov processes. I will show a convergence study of the algorithm close to dynamical phase transitions, exploring the speed of convergence as a function of the learning rate and the effect of including transfer learning in parameter space. As a test example for the optimal perfomance of the algorithm, I will discuss the mean degree of a uniform random walk on Erd¨os–R´enyi random graphs, which appears to show a delocalisation-localisation transition in the infinite size limit.