|
Résumé |
The Kardar–Parisi–Zhang equation, introduced in 1986, is a paradigmatic model for the random growth of interfaces. It lies at the center of a vast universality class that describes out-of-equilibrium fluctuations in a variety of growth and transport phenomena. It appears ubiquitously, sometimes in mysterious ways, as recently found in quantum spin transport.
I will review recent advances in physics and mathematics that have led to an almost complete characterization of fluctuations in the one-dimensional KPZ class. Surprising connections with random matrix theory have emerged, as well as with the statistics of extreme events.
I will show how a unifying framework based on determinantal point processes naturally emerges and allows one to make predictions in yet another domain of physics: non-interacting cold fermions in traps. Some of these predictions, concerning the spatial organization induced by Pauli’s exclusion principle, have been tested in a recent experiment, which I will describe. |
