Vlada Limic received her undergraduate degree in mathematics from the University of Zagreb in 1994, and her PhD from the University of California at Berkeley in 1998. She held postdoctoral positions at UC San Diego and at Cornell University. In 2002, Vlada became a junior professor at the University of British Columbia in Vancouver. In 2006, she joined the CNRS (French National Centre for Scientific Research) and worked for six years at the Université de Provence in Marseilles. She was promoted in 2012 to a CNRS research director, initially affiliated to the mathematics department at Paris-Sud Orsay. Starting 2017 her affiliation is the mathematics department at the University of Strasbourg. Most of Vlada’s research is either on coalescent processes or on models with reinforcement. In both areas she contributed to solving difficult problems. She was a recipient of the Alfred P Sloan Research Fellowship in 2005, and of the Friedrich Wilhelm Bessel research award from the Alexander von Humboldt Foundation in 2016. This Medallion lecture was given at the IMS Annual Meeting in London.

Multiplicative coalescent related processes

The seminal work by David Aldous introducing the standard multiplicative coalescent, and proving that it is the scaling limit of close-to-homogeneous near-critical random graph component sizes was published twenty-five years ago. His analysis relied on a certain graph exploration process, analogous to a one-dimensional random walk. In the meantime both kinds of processes (multiplicative coalescents, and various random-walk-type exploration processes) became quite popular in the literature.

The aim is to describe some atypical studies involving these kinds of processes, or their relatives. In particular, by the end of the talk you will be able to understand why non-standard multiplicative coalescents may emerge in scaling limits of certain “locally” inhomogenous near-critical graphs (an old result), and why a new and more complicated process, called the interacting multiplicative coalescents, emerges for certain near-critical class-wise homogeneous graphs (a new result in a joint paper with Vitalii Konarovskyi). Some highlights of related studies, available as preprints or still in progress, will be mentioned in passing.