**统计与管理学院2017年学术报告第61期****【主 题】****Scaling limits of critical random graphs****【报告人】**Nicolas Broutin 教授Université Paris VI（巴黎第六大学）

**【时 间】**2017年10月26日（星期四）15:00-16:00**【地 点】**上海财经大学统计与管理学院大楼一楼1208会议室【

**摘 要**】For many models of random graphs, as one increases the density of edges, one usually observes a sudden change in structure at a critical density that depends on the model: precisely at that point, a macroscopic "giant component" containing a linear proportion of the nodes starts to emerge. The structure of the graph at the "critical" point of the phase transition does not yet contain any acroscopic component, but many large ones at an intermediate scale, that will quickly merge into a single "giant". Understanding the phase transition and the structure of the "critical" random graphs that one observes just before the birth of the giant has since the first papers of Erdos and Renyi been one of the most fascinating topics in random graphs, and more generally in models related to statistical physics.I will paint the big picture and to review some results about some results about scaling limits of such "critical" random graphs, in particular about their metric structure in some specific models such as the classical Erdos-Renyi random graphs, but also inhomogeneous random graphs.

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**嘉宾简介**】Nicolas Broutin is a Visiting Associate Professor of Mathematics at NYU Shanghai. Between 2008 and 2017, he was a researcher at Inria Paris. He has just joined Université Pierre et Marie Curie - Paris 6 as a professor. He holds a MEng from Ecole Polytechnique (Paris), and a PhD from McGill University. His research interests include probability, random structures and algorithms, especially random graphs.