The school will focus on some stochastic aspects of mathematics and on algorithms used in this context. More precisely, classical random structures such as Markov chains, random walks, discrete combinatorial structures, random texts, chaotic dynamical systems will be considered and some tools to study them, mainly analytic combinatorics, will be given.
A course will be given on finite Markov chains for optimization with applications to famous problems such as Traveling Salesman Problem and Scheduling. Another course will be on random walks with related topics such as Brownian motion, Lattice walks and structural properties of the associated generating functions. A course will also be provided on bioinformatics and linguistics with use of methods such as formal languages, automata and use of generating functions. Moreover, a course will be dedicated to the analytic tools used for the previous course which includes Cauchy integral, combinatorics of structures, generalized central limit law, Mellin integral.
Chaotic dynamical systems will be considered as random source. A tutorial for the free computer algebra system SageMath and a course on statistics language R will be scheduled.
Langue officielle de l'école : anglais