Overview 

Random graphs are a cornerstone of modern probability theory, celebrated not only for their mathematical elegance but also for their applications in modeling complex networks. In the early 2000s, I. Benjamini and O. Schramm introduced a groundbreaking framework that endowed the set of locally finite rooted connected graphs with the structure of a Polish space, known as the local topology. This summer school aims to explore the framework of local limits of random graphs, focusing on key concepts such as Benjamini-Schramm (or unbiased) limits, unimodularity, and their most significant applications. 

The program will feature lectures by Nicolas Curien (Professor at Paris-Saclay University) and Justin Salez (Professor at Université Paris-Dauphine), complemented by interactive problem sessions. Students will work in small groups under the guidance of teaching assistants, who are active researchers in the field. The school will also include daily evening sessions for informal discussions, research talks by senior researchers, and opportunities to network over food and drinks. 

 

Here are our 34 summer graduate school students.
Thanks to all of you !

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Daily schedule

Each day will consist of two lectures delivered by leading experts, two problem sessions where students will collaborate in small groups and evening sessions featuring research talks and informal discussions.

  • 09:00 - 09:30 : Breakfast
     
  • 09:30 - 11:30 : Lecture 1
     
  • 11:30 - 12:00 : Discussions
     
  • 12:00 - 13:30 : Lunch
     
  • 14:00 - 15:30 : Lecture 2
     
  • 15:30 - 16:00 : Tea and Coffee
     
  • 16:00 - 18:00 : Problem Session lead by TAs and lecturers

Prerequisites

To fully benefit from the program, students should have a solid foundation in probability theory, including:

  • Convergence of measures (convergence in law in Polish spaces).
  • Poisson processes, countable Markov chains, and martingales (convergence theorems).
  • Basic notions in statistics.

 

References

Recommended references include:

  • Jean-François Le Gall's Measure Theory, Probability, and Stochastic Processes.
  • Chapter 1 of Patrick Billingsley's Convergence of Probability Measures.
  • Rick Durrett's Probability: Theory and Examples.

Familiarity with graph theory, discrete potential theory (random walks on graphs), and ergodic theory is advantageous but not mandatory. Key results from these areas will be reviewed during the lectures. 

Lecturers

Teaching assistants

Local organizers

 

Lecture Notes

Chapter 1 Chapter 2 Chapters 7 to 9

 

 

Video recordings

All video recordings concerning the school will be available at the link below :

https://www.imo.universite-paris-saclay.fr/~benjamin.auder/local_limit_random_graphs.html
Short link: http://bit.ly/3Htcm22
 

 

Practical information

Application procedure for international students

International students interested in applying should visit the Summer Graduate Schools homepage. Upon acceptance, an invitation letter will be sent to you.

Application Deadline: March 14, 2025 

Registrations are closed

Application procedure for local students

Local students (those not requiring accommodation) who wish to receive an invitation to attend are requested to send an email to contact@fondation-hadamard.fr.

Application Deadline: April 11, 2025.

Registrations are closed

Venue

The summer school will take place at the Orsay Mathematics Institute, located on the campus of Paris-Saclay University, approximately 35km south of Paris. 

Accomodation

Non local students will be housed in single-occupancy rooms at the  Les Jardins de Fleming, 21 rue andré Maginot, Orsay.  

Meals

  • International students : On weekdays breakfast, lunch, and dinner will be provided. On weekends only breakfast and dinner will be provided.
  • Local students : On weekdays breakfast and lunch will be provided. On weekends, no meals will be provided.

 

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