Abstract:
Boole's transformation is a typical example of infinite ergodic transformation.
In this talk we consider occupation times of Boole's transformation under a tied-down condition,
that is, the condition the orbit returns to a reference set with finite measure at the final observation time.
We explain the uniform distribution appears as the limit distribution.
This result is similar to the uniform law for Brownian bridge.
This talk is besed on joint work with Jon Aaronson (Tel Aviv University).