Near-critical random graphs, a probabilistic approach

The Erdös-Rényi random graph was defined in a seminal 1973 paper by Erdös and Rényi, an English translation of which appeared in 1976. The model is of percolation type, and exhibits a phase transition as the number of particles (vertices, points) diverges, and the connective probability (of each pair of vertices) is about its reciprocal. Since 1970's random graphs have been widely studied, initially mostly by combinatorists. In 1997 the probabilistic approach began with a famous work by Aldous on random graphs and the standard (i.e. Aldous') multiplicative coalescent. The talk is intended to serve as an introduction to this research direction. It will try to explain the core of the 20 year old results, as well as certain recent improvements and developments. In anticipation of a mixed audience (analysits+probabilists+possibly others?) the talk will resemble more to a colloqium than to a probability working seminar.