Laboratoire de Physique Théorique
Toulouse - UMR 5152

I will first introduce the Google Matrix of the WWW and PageRank and CheiRank algorithms. I will then construct the Google matrix of the World Trade Network (using the United Nations Commodity Trade Statistics Database) and analyze its properties for various trade commodities for all countries and all available years from 1962 to 2009. For the world trade this ranking treats all countries on equal democratic grounds independent of country richness. Still this method puts at the top a group of industrially developed countries for trade in all commodities. Our study establishes the existence of two solid state-like domains of rich and poor countries which remain stable in time, while the majority of countries are shown to be in a gas like phase with strong rank fluctuations. A simple random matrix model provides a good description of statistical distribution of countries in two-dimensional ranking plane. The comparison with usual ranking by export and import highlights new features and possibilities of our approach.