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Random walks with memory typically involve rules where a preference foreither revisiting or avoiding those sites visited in the past are introducedsomehow. Such effects have a direct consequence on the statistics offirst-passage and subsequent recurrence times through a site; typically, apreference for revisiting sites is expected to result in a positive correlationbetween consecutive recurrence times. Here we derive a continuous-timegeneralization of the random walk model with preferential relocation to visitedsites 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 analyticaltreatment allows us to (i) observe the existence of an asymptotic logarithmic(ultraslow) growth for the mean square displacement, in accordance to theresults found for the original discrete-time model, and (ii) confirm theexistence of positive correlations between first-passage and subsequentrecurrence times. This analysis is completed with a comprehensive numericalstudy which reveals, among other results, that these correlations betweenfirst-passage and recurrence times also exhibit clear signatures of theultraslow dynamics present in the process.

Recurrence time correlations in random walks with preferential relocation to visited places