MATH-519 / 5 credits

Teacher: Aru Juhan

Language: English


Summary

This year we will be looking at topics in high-dimensional probability, i.e. properties of large random systems.

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 (for example, the Bloc "Science de Base" in EPFL Mathematics Bachelor's program).

Recommended courses

Some interest in geometry and combinatorics might turn out to be useful

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.

Resources

Bibliography

A large chunk of the course is covered in Ramon van Handel "Probability in high dimension" available on his webpage.

Notes/Handbook

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

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Computational linear algebra
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Computational linear algebra
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Computational linear algebra
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11  MAA110  
11-12    
12-13     
13-14  MAA110  
14-15    
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     

Wednesday, 10h - 12h: Lecture MAA110

Wednesday, 13h - 15h: Exercise, TP MAA110