Section: New Results

Randomness and ergodicity: compressibility

Participant : Mathieu Hoyrup.

In [25] , we solve a problem that has been open for 15 years. It relates three notions of complexity and information: Shannon information and entropy, Kolmogorov algorithmic information and Martin-Löf randomness. We obtain that the limit rate of compressibility of a random sequence equals the entropy of the underlying ergodic measure. This result is the achievement of several years of development.