Return- and hitting-time limits for rare events of null-recurrent Markov maps

FRANÇOISE PÈNE, BENOÎT SAUSSOL, ROLAND ZWEIMÜLLER
2015 Ergodic Theory and Dynamical Systems  
We determine limit distributions for return- and hitting-time functions of certain asymptotically rare events for conservative ergodic infinite measure preserving transformations with regularly varying asymptotic type. Our abstract result applies, in particular, to shrinking cylinders around typical points of null-recurrent renewal shifts and infinite measure preserving interval maps with neutral fixed points.
doi:10.1017/etds.2015.38 fatcat:7ofm5iup4rclpgiyxz4ysjgkpq