M2 – Probability and Random Models (PMA)

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Here is the detailed official introduction of the M2-PMA 2025-2026 (French version) [brochure 2025-2026] and the official website of M2-PMA [web].

A brief introduction to PMA

M2-PMA is basically one of the strongest M2 programs in France for pure probability or Stochastic Processes (the other being Université Paris-Saclay’s M2 Mathématiques de l’aléatoire, of course we also can’t ignore the rising new force of Université Paris Dauphine-PSL’s M2 MATH. This M2 has 3 majors - “Stochastic process”, “Applied probablity” and “EDProba”.

M2-PMA admits about 20–30 people each year, including some ENS-PSL normaliens or normaliennes, engineers from X, and some very strong international students, for example from the University of Science and Technology of China (the Sino-French program). Most of them choose the Major in Stochastic Processes — roughly 20 people.

In the 2025–2026 academic year, M2-PMA added a major called “EDProba” which means “PDE + Probability.” This major is jointly offered with M2 Modélisation. The first semester has 15 ECTS in Modélisation and 15 ECTS in PMA. The course options for the following semester are also fairly fixed, and there isn’t as much freedom for EDProba students in that semester (look at Brochure 2025-2026). If you are enrolled as a Modélisation student, you will ultimately receive the Modélisation diploma, rather than the PMA diploma.

Application recommendations or conditions

I was admitted to M2-PMA from Sorbonne University M1 via eCandidat (Sorbonne University’s application procedure). My M1 courses were:

First semester:

1. Advanced Probability
2. Statistics

Second semester:

1. Advanced Functional Analysis and Variational Calculus
2. Stochastic Calculus and Stochastic Control
3. M1 thesis

In my personal opinion and based on the information I have, for students who have already registered for M1 Mathematics and Applications at SU, admission to M2-PMA places the greatest importance on advanced probability (with Thierry Lévy) grades; anything above 14/20 is very competitive. This course is mainly the prerequisite material for the M2-PMA program, including conditional expectation, martingales, convergence of martingales, and Markov chains. (the specific content is almost identical to Jean-François Le Gall’s book “Measure Theory, Probability, and Stochastic Processes”). To my knowledge, starting in 2025–2026, the M1 program was reformed. The former course “Probabilités approfondies” was split into

• “Probabilités approfondies (UM4MA311)”
• a part of “Martingales et contrôle stochastique (UM4MA280)”

My PMA course selection or materials

Here is my M2-PMA course selection (Major stochastic process)

Semester 1

• Stochastic Calculus and Diffusion Processes
• Markov I (Discrete Markovian Models + Markov Processes and Applications + Poissonian Clouds)
• Convergence of Measures, Large Deviations, Percolation
• Markov II (Clouds Theory, Levy Processes, and Excursions)

Semester 2

• Integrable probability & The KPZ (Kardar-Parisi-Zhang) Universality Class
• Determinantal processes, random matrices and hyperuniformity
• Rough Paths and Stochastic differential equation
• Internship (Master thesis) at Laboratory