Chaire Aisenstadt                  


Aisenstadt Chair



Professor Svante JANSON

(Uppsala University)


Une série de conférences / A series of lectures 


Cette conférence s'adresse à un large auditoire / Suitable for a general audience


Le vendredi 17 octobre 2008  / Friday, October 17th, 2008

16h00 / 4:00 p.m.

Salle / Room 1360                                                                                                             

Pavillon André-Aisenstadt

Université de Montréal

2920, ch. de la Tour


Random Graphs: New models and the Internet

Random graphs have been more or less successfully applied to many real-life problems. One important example is the Internet, which can be regarded as a very large graph. This graph can in practise not be described exactly, and to study various properties, such as vulnerability to intentional or accidental disruptions, it is natural to study random models


However, the classical random graph models are often too homogeneous to be good approximations. In particular, in the Internet and many other real-life examples, it is observed that the vertex degrees (number of adjacent edges) vary a lot, often with a power-law distribution of the high degrees. This has served as a source of inspiration for random graph theorists, and during the last 10 years, a number of new random graph models have been introduced and studied in order to mimic the Internet or other similar graphs.


This illustrates that not only can mathematics be useful for applications; conversely, applications can stimulate new theoretical developments.

I will give some examples from the Internet and describe some different random graph models that have been proposed.



Un café sera servi à 15h30 et une réception suivra la conférence au Salon Maurice-l'Abbé – salle 6245

Coffee will be served at 3:30 p.m. and there will be a reception after the lecture in Salon Maurice-l'Abbé – Room 6245



Random Graphs

Several different models of random graphs will be introduced and studied, starting with the classical Erdšs-Renyi model. Some of the discussed models (and examples of people that have worked on them) are: random graphs with given vertex degrees  (Molloy and Reed), preferential attachment models (Barabasi and Albert), the CHKNS model  (Callaway, Hopcroft, Kleinberg, Newman and Strogatz), and the inhomogeneous model  (Bollobas, Janson and Riordan).


The emphasis will be on the existence of a giant component, the vertex degree distribution, and the susceptibility (mean size of the component containing a random vertex). I will use various probabilistic methods, including branching processes and stochastic processes.



Le lundi 20 octobre 2008  / Monday, October 20th, 2008

Le mercredi 22 octobre 2008 / Wednesday, October 22nd, 2008

Le jeudi 23 octobre 2008 / Thursday, October 23rd, 2008


16h00 / 4:00 p.m.

Salle / Room 6214

Pavillon André-Aisenstadt

Université de Montréal

2920, ch. de la Tour

Un café sera servi à 15h30 au Salon Maurice-l'Abbé – salle 6245

Coffee will be served at 3:30 p.m. in Salon Maurice l'Abbé – Room 6245