This article exists first and foremost to contribute to a tribute to Patrick
Cattiaux. One of the two authors has known Patrick Cattiaux for a very long
time, and owes him a great deal. If we are to illustrate the adage that life is
made up of chance, then what could be better than the meeting of two young
people in the 80s, both of whom fell in love with the mathematics of
randomness, and one of whom changed the other’s life by letting him in on a
secret: if you really believe in it, you can turn this passion into a
profession. By another happy coincidence, this tribute comes at just the right
time, as Michel Talagrand has been awarded the Abel prize. The temptation was
therefore great to do a double. Following one of the many galleries opened up
by mathematics, we shall first draw a link between the mathematics of Patrick
Cattiaux and that of Michel Talagrand. Then we shall show how the abstract
probabilistic material on the concentration of product measures thus revisited
can be used to shed light on cut-off phenomena in our field of expertise,
mathematical statistics. Nothing revolutionary here, as everyone knows the
impact that Talagrand’s work has had on the development of mathematical
statistics since the late 90s, but we’ve chosen a very simple framework in
which everything can be explained with minimal technicality, leaving the main
ideas to the fore.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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