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].
- ...