## 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.