Stochastic seminar: Musical chairs dynamics

N players are waiting on the real line. When the music starts, all of them move upwards and start dancing in the upper complex plane. After a time, one of them leaves the game and diverges to infinity, whereas the others go slowly back to (N-1) locations on the real line. End of the game. We will present a random matrix model whose eigenvalues evolve according to this musical chairs dynamic, and establish a few rigorous results. In particular, we will (partially) answer the natural question: how long do they dance before one of them is eventually ejected?. Joint work with L. Erds.