Yariv Kafri, Technion, Israel

Statistics of Rare Events and Large Deviations (13.5h)

1. The mathematical question through a simple example

2. Why study rare events?

Motivations from physics, population dynamics, reactions and more

3. A crash course on stochastic processes:

Master equation

Stochastic differential equations

Fokker-Planck

Path integrals

4. Rare events in weak-noise finite dimensional systems: calculating the large deviation function

Motivations

From path integrals to the underlying Lagrangian and Hamiltonian structure

Time reversal symmetry and detailed balance

Basic singular structures

Transport models and non-trivial correlations

5. Rare events in macroscopic diffusive systems

From microscopic models to field theories

Long-range correlations in out of equilibrium diffusive systems

From path integral to the underlying Lagrangian and Hamiltonian structure

The structure of the large deviation function

Large deviations of currents

6. Summary and outlook