Topics in probability

Summary

This year we will be looking into probabilistic study of some models of mathematical physics.

Content

Keywords

High-dimensional probability, concentration of measure, Gaussian processes, phase transitions, universality

Learning Prerequisites

Required courses

Mathematics Bachelor's level knowledge of analysis, linear algebra and probability.

Recommended courses

Knowledge of basic measure theory will simplify your life a lot. Interest in mathematical physics, combinatorics and geometry is of use.

Important concepts to start the course

Probability space, random variable and random vector, expectation, Gaussian random variables.

Teaching methods

Lectures, exercise classes. Maybe on some topics we also try a flipped format, where you can give a presentation.

Assessment methods

Most likely an oral exam, but in case of presentations, these would also count towards the final grade.

Resources

Bibliography

Will be discussed in class

Notes/Handbook

There might be partial notes, though the book is excellent.

Moodle Link

• https://go.epfl.ch/MATH-519