Bernoulli trial under subsystem restarts: Two competing searchers looking for a target

We study a pair of independent searchers competing for a target under restarts and find that introduction of restarts tends to enhance the search efficiency of an already efficient searcher. As a result, the difference between the search probabilities of the individual searchers increases when the system is subject to restarts. This result holds true independent of the identity of individual searchers or the specific details of the distribution of restart times. However, when only one of a pair of searchers is subject to restarts while the other evolves in an unperturbed manner, a concept termed as subsystem restarts, we find that the search probability exhibits a nonmonotonic dependence on the restart rate. We also study the mean search time for a pair of run and tumble and Brownian searchers when only the run and tumble particle is subject to restarts. We find that, analogous to restarting the whole system, the mean search time exhibits a nonmonotonic dependence on restart rates.