  Random walks with memory typically involve rules where a preference for
either revisiting or avoiding those sites visited in the past are introduced
somehow. Such effects have a direct consequence on the statistics of
first-passage and subsequent recurrence times through a site; typically, a
preference for revisiting sites is expected to result in a positive correlation
between consecutive recurrence times. Here we derive a continuous-time
generalization of the random walk model with preferential relocation to visited
sites proposed in [Phys. Rev. Lett. 112, 240601] to explore this effect,
together with the main transport properties induced by the long-range memory.
Despite the highly non-Markovian character of the process, our analytical
treatment allows us to (i) observe the existence of an asymptotic logarithmic
(ultraslow) growth for the mean square displacement, in accordance to the
results found for the original discrete-time model, and (ii) confirm the
existence of positive correlations between first-passage and subsequent
recurrence times. This analysis is completed with a comprehensive numerical
study which reveals, among other results, that these correlations between
first-passage and recurrence times also exhibit clear signatures of the
ultraslow dynamics present in the process.
