# Integrable Probability

## M2 Mathématiques avancées, parcours probabilités, Lyon 2018-2019/2019-2020

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### Material

The course is based on chapters 1 and 2 of the book *The
Surprising Mathematics of Longest Increasing Subsequences* by
Dan Romik. It is available
online here.

In the first part based on chapter 1, we stayed close to the
book. For chapter 2 we are slightly diverging from it: here are some
preliminary lecture notes (work in
progress).

### Exercises

Here are some exercises (in French) related
to the material presented in the lectures.

### Related papers

Here are some papers related to the topics of the course.

- D. Aldous and P. Diaconis,
*Hammersley's interacting
particle process and longest increasing subsequences*,
Probab. Theory
Related Fields 103 (1995), no. 2, 199–213.
- K. Johansson,
*Shape fluctuations and random matrices*,
Comm. Math. Phys. 209
(2000), no. 2,
437–476, arXiv:math/9903134
[math.CO]. See also Chapters 4 and 5 of Romik's book.
- A. Okounkov and N. Reshetikhin,
*Correlation function of
Schur process with application to local geometry of a random
3-dimensional Young
diagram*, J. Amer. Math. Soc. 16
(2003), no. 3,
581–603, arXiv:math/0107056
[math.CO].
- M. S. Kammoun,
*Monotonous subsequences and the descent
process of invariant random permutations*,
Electron. J. Probab.,
Volume 23 (2018), paper
no. 118, arXiv:1805.05253
[math.PR].
- A.-L. Basdevant and L. Gerin,
*Longest increasing paths
with
gaps*, arXiv:1805.09136
[math.PR].
- ...