Instructor: Igor Kortchemski. The course is taught is English.

Random phenomena are modelled using modern probability theory, defined in the 1930s by Kolmogorov using measure theory as a cornerstrone. The theoretical understanding of these foundations is an asset to forge intuition, to understand the objects of interest and to mobilize them in an applied or theoretical framework. Without any necessary prerequisites, the aim of this EA will be to take the time to consolidate some of the foundations of probability related to measure theory in an accessible way, emphasizing ideas and giving several applications on important models in probability theory (such as percolation, random walks in random media, random matrices, Brownian motion, random fractals, random graphs, etc.).

This course is designed for an audience with a variety of interests: on the one hand, it may be of interest to students willing to study probability in greater depth, and on the other hand, it may be of interest to students interested in business applications (a good understanding of probability theory is essential to know how to navigate and innovate in the world of applications).

Evaluation is done through an oral presentation of a research paper or a significant application.

Lecture notes and exercise sheets

Moodle webpage of the course.  

  • Lecture notes  
  • Exercise sheets
  • Progression

    The teaching takes place on Tuesday, from 13h30 to 15h.

    The course contains a "lecture" part and an "exercise" part. Given the context, the "lecture" part will be organised in a "flipped classroom" way: at week n, lecture notes are given (covering the content of the theme of week n+1), together with an exercise. You are asked to read these lecture notes for week n+1 try to solve the exercise and upload your work on Moodle. At week n+1, the key elements of the lecture notes which were given at week n will be discussed, the exercise will be discussed, and then a tutorial session with new exercises will take place.

    Provisional programme:

    Evaluation

    Evaluation is done through an oral presentation of a research paper or a significant application.

    List of presentations