Notes

• Notes on the article "Quantitative measure equivalence between amenable groups" (by Delabie, Koivisto, Le Maître and Tessera). We give a proof of their main theorems (about obstructions under quantitative measure equivalence) in the particular and easier case of orbit equivalence.
• These notes have been written to complete my talks in the working group on ergodic theory:
  • Notes presenting a state of the art in quantitative orbit equivalence, and some details about my recent work on odomutants (with an appendix about basics in ergodic theory)
  • Introduction to Kakutani equivalence
  • Notes (in french) on Kerr and Li's theorem ("entropy is preserved under Shannon orbit equivalence") in the case of p.m.p. ℤ-actions
• Here you can find my master thesis (in french) about Shannon orbit equivalence, supervised by François Le Maître. It contains an overview about orbit equivalence and some dynamical systems such as rank-one systems and more particularly odometers.