Master course, lecture notes:
- Lecture 1 and addendum
(Galton-Watson process), exercise
given at the end of the lecture, its
solution.
- Lecture 2 (plane trees and the
cycle lemma, exercise given at the
end of the lecture, its
solution.
- Lecture 3 (proof of the cyclic
lemma, generating series and Lagrange's inversion formula), exercise
given at the end of the lecture, its
solution.
- Lecture 4 (end of the proof of
Lagrange's inversion formula, definition of Galton-Watson trees), exercise
given at the end of the lecture, its
solution.
- Lecture 5 (coding Galton-Watson
trees by random walks), exercise
given at the end of the lecture, its
solution.
- Lecture 6 (Local limit
theorem).
- Lecture 7 (applications of the
local limit theorem and local convergence of Galton-Watson trees), exercise
given at the end of the lecture, its
solution.
- Lecture 8 (height process of a
forest, scaling limit of a random walk), exercise
given at the end of the lecture, its
solution.
- Lecture 9 (Recurrence criteria
for an integer valued random walk, space of continuous functions on
[0,1])), exercise given at the end
of the lecture, its
solution.
- Lecture 10 (théorème
d'invariance de Donsker).
- Lecture 11 (scaling limit of
the height process of a forest of trees, Brownian bridge).
- Lecture 12 (Brownian bridge,
Brownian excursion, scaling limit of the height process of a large
Galton-Watson trees).
