Tuesday, August 3: A very basic introduction to the replica method, from the point of view of a physicist and from a mathematician. Lecture notes welcomed if someone take them! Basically, I will follow this short latex notes. The video is here!
For those who wanna go beyond, try a slightly more difficult (but still easy) exercice and repeat both the physics approach and the rigorous one for the rank-one matrix factorization problem ( short latex notes or the more detailed one here for the replica computation.
References: * Marc Mézard and Andrea Montanari, Information, Physics, and Computation, Florent Krzakala, Jiaming Xu, Lenka Zdeborová, arXiv:1603.08447, Ahmed El Alaoui, Florent Krzakala, arXiv:1801.01593, Jean Barbier, Nicolas Macris, arXiv:1901.06516.
Thursday, August 6: I used these slides to review some of the physics-related results on linear models, on kernels methods and random projections. The video is here!
References: Aubin, FK, Lu, Zdeborova arXiv:2006.06560, Gerarce, Loureiro, FK, Zdeborova: < a href="https://arxiv.org/abs/2002.09339">arXiv:2002.09339, Mignacco, FK, Lu, Zdeborova arXiv:2002.11544. A great classical and readable reference is the 1995 short review from Manfred Opper.
Tuesday, August 11: I used these slides to review some of the physics-related results on constraint satitsfaction problems, in particular q-colouring on random graphs. The video is here!
The coloring problem is a good example to learn the cavity method. the paper I wrote with Lenka in 2007 is self-contained and a good introduction to the subject. There are many good references to learn the cavity method, including F. Zamponi's notes or the Book from Mézard and Montanari.
Discussion on the landscaoe of the problems appeared in particular in Krzakala-Kuchans https://arxiv.org/pdf/cond-mat/0702546.pdf, Lenka Zdeborova's phd thesis, Lenka and I's paper on following states and many other references.