The Brownian motion is the scaling limit of random walks where the step distribution has finite second moment. Various random objects constructed from the Brownian motion, e.g., the Brownian continuum random tree and the Brownian map, arise naturally in the study of random trees, graphs, and maps. In the first talk, we will give a gentle introduction to these objects. In the second talk, we will discuss some recent advances in establishing certain Brownian objects as the scaling limits of different models of random discrete structures.

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Last updated: 19 Jul 2024