Hitting and escaping statistics: mixing, targets and holes

Henk Bruin, Mark F. Demers, Mike Todd

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


There is a natural connection between two types of recurrence law: hitting times to shrinking targets, and hitting times to a fixed target (usually seen as escape through a hole). We show that for systems which mix exponentially fast, one can move through a natural parameter space from one to the other. On the other hand, if the mixing is subexponential, there is a phase transition between the hitting times law and the escape law.
Original languageEnglish
Pages (from-to)1263-1298
Number of pages36
JournalAdvances in Mathematics
Early online date22 Feb 2018
Publication statusPublished - 13 Apr 2018


  • Hitting time statistics
  • Open systems
  • Escape rates
  • Recurrence
  • Mixing rates


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