GĂ©rard Ben Arous. Courant Institute of Mathematical Sciences, New York, USA

Universal features of slow dynamics in random media (10.5h)

1. A general introduction to slow random dynamics.

2. Elementary probabilitic tools: Sums and extrema of i.i.d variables, a quick survey.

3. The Bouchaud trap models: aging and scaling limits for the simplest case of the complete graph.

4. The Bouchaud Trap models on the cubic lattice.

5. Trapping and transport: The biased random walk on supercritical trees.

6. Trapping and transport: recent progress on biased random walks on supercritical percolation clusters.

7. The general trapping models and their scaling limits in one dimension : The Randomly Trapped Brownian Motion (RTBM).

8. The RTBM as the scaling limits for random walks on critical trees.

9. Trapping and aging for glassy dynamics: the Random Hopping Time (RHT) dynamics for the Random Energy Model (REM).

10. Trapping and aging for glassy dynamics: the RHT dynamics for the general spin glasses.

11. Trapping and aging for glassy dynamics: recent progress on Glauber dynamics for the REM.

12. Trapping and aging for glassy dynamics: Complexity and Langevin dynamics for the spherical spin glasses.

13. Open questions and perspectives.