Chaire Aisenstadt 2008-2009 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 |