Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks

Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently the presence some obstacles or constraints. A somewhat class focuses on optimal distributions weights which, for a given connection topology, maximize kind flow minimize cost function. We show that sets can be approached through an analysis large-deviation functions random walks. Specifically, study ensembles trajectories allows us find paths, design weighted by means auxiliary stochastic process (the generalized Doob transform). In contrast standard approaches, not limited must necessarily optimize Paths fact tailored statistics time-integrated observable, which may activity current, local marking passing walker node link. illustrate this idea with exploration obstacles, networks flows under constraints observables.