Preliminaries: review of percolation, interacting particle systems, concentration inequalities [1,2].
The KPZ universality class. Last-pass percolation, totally asymmetric exclusion. [3].
The phenomenon of measurement concentration. Concentration inequalities for functions of independent random variables. (Special lectures by Gábor Lugosi, Universidad Pompeu Fabra/Barcelona [4].
Review of the theory of Markov chains. Advanced topics in mixing and arrival times for particle systems. (Includes special lectures by Perla Sousi – Cambridge and Alexandre Stauffer – Bath.) [5,6].
High-dimensional probability topics: introduction to empirical processes, chaining and continuity of Gaussian processes, compressed sensing and high-dimensional covariance matrices. [4,7,8].
Introduction to high-dimensional statistics: LASSO and variants (Special lectures by Alexandre Belloni – Duke). [9].

References:
[1] T. Liggett. Interacting Particle Systems. Springer (2004).
[2] G. Grimmett. Probability on Graphs. Cambridge (2010).
[3] Ivan Corwin. “The Kardar-Parisi-Zhang equation and universality class”. Random Matrices: Theory and Appliations Vol. 1 (2014).
[4] S. Boucheron, G. Lugosi and P. Massart. Concentration Inequalities: a nonasymptotic theory of independence. Oxford (2013).
[5] D. Levin, Y. Peres and E. Wilmer. Markov chains and mixing times. AMS (2008).
[6] D. Aldous and J. A. Fill. Reversible Markov chains and random walks on graphs. Lecture notes.
[7] M. Talagrand. The generic chaining. Springer (2006).
[8] R. I. Oliveira. “The lower tail of random quadratic forms”. Preprint.
[9] A. Belloni. Class notes.
* Basic syllabus. The teacher has the autonomy to make any changes.