Scaling limits for self-interacting random walks and diffusions
Lectures at the Berlin-Zürich Summer School on
''Stochastic Models of Complex Processes''
Chorin, Germany, August 31 to September 4, 2009
(Hand written lecture notes)
1. Introduction, motivation, phenomenological (non-rigorous) arguments,
models, conjectures, preview of resuls
(5.3 Mb)
2. Limit theorems for the "Myopic" (or "True") Self-Avoiding Random Walk
in 1d: time-to-the 2/3 scaling
(8.8 Mb)
3. Construction of the 1d scaling limit: the "True Self-Repelling Motion".
(10.0 Mb)
4. The environment as seen from the moving particle. The stationary regime.
The appropriate Hilbert spaces and the infinitesiaml generators.
(11.1 Mb)
5. CLT for additive functionals of stationary (and ergodic) Markov processes:
"Kipnis-Varadhan technology", non-reversible setup. Relaxing Varadhan's "sector condition".
(7.7 Mb)
6. CLT for self repelling random walks and diffusions in 3d: applying "Kipnis-Varadhan
technology"
(4.3 Mb)
References