Minicourses

We will have 2 minicourses on Random Graphs and Networks.

• Richard Durrett (Cornell)
  Random Graphs Dynamics
  Abstract: This course will be a rapid tour of my book recently published by Cambridge University Press. We will emphasize the study of processes taking place on random graphs and mention a number of open problems.
  
  
• José Fernando Mendes (Aveiro)
  Random Networks
  Abstract: I my course I plan to touch the following aspects of Science of Complex Networks:
  - I will discuss the modern state of art of the physics of the evolving networks and the great role of the general principle – popularity is attractive.
  - The k-core decomposition was recently applied to a number of real-world networks. Rich k-core architectures of real networks were revealed. We find the structure of k-cores, their sizes, and their birth points — the bootstrap percolation thresholds. I will show a derivation of exact equations describing the k-core organization of a randomly damaged uncorrelated network with an arbitrary degree distribution. This allows us to obtain the sizes and other structural characteristics of k-cores in a variety of damaged and undamaged random networks and find the nature of the k-core percolation in complex networks. These general results will be applied to the classical random graphs and to scale-free networks, in particular, to empirical router-level Internet maps.
  - I will analyze the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the spectra of networks with a local tree-like structure are presented. A simple approximation will be proposed, and in the framework of effective medium approximation, calculate spectra of various graphs analytically. Show that spectra of locally tree-like random graphs gives a good description of the spectral properties of real-life networks like the Internet.

2007 ~ University of São Paulo (USP), Institute of Mathematics and Statistics (IME)
Created and maintened by Thiago Rodrigo Carneiro.