When modeling random walks on the lattice, null recurrence implies that states are visited infinitely often but with infinite mean return time.

Students learned how to derive a recurrence relation from the initial terms of a sequence.

Students often struggle to derive closed-form solutions from recurrence relations without practice.

After three miscarriages, the recurrent aborter consulted her specialist about treatments to prevent future pregnancy loss.

Clinicians should provide counseling to recurrent aborters to address the physical and emotional effects of repeated pregnancy termination.

The recurrent nova in the distant galaxy surprised astronomers when it brightened again after several decades.

Several recurrent novae were observed by amateur astronomers over the last decade, providing valuable data for models of binary star evolution.

In the Markov chain model, the null recurrent state returns with probability one but has an infinite expected return time.

For our Markov chain, every positive recurrent state has a finite expected return time and thus guarantees ergodicity in its communicating class.

Scientists debated whether the recurrent slope lineae on the Martian hills were formed by briny flows or dry granular movements.