Local and global convergence of random trees

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Random trees arise naturally in a wide range of contexts, from the analysis of algorithms and data structures to models in statistical physics and evolutionary biology. Understanding their large-scale behavior not only reveals connections between combinatorics, probability, and geometry but also sheds light on universal structures emerging in complex systems.

This mini-course explores the limiting properties of random trees. We begin by developing combinatorial techniques for sampling random trees. From there, we investigate their asymptotic structure using two powerful frameworks: global convergence in the Gromov–Hausdorff topology, capturing the tree’s macroscopic shape, and local convergence in the Benjamini–Schramm topology, describing the limiting neighborhood structure around a typical node.

Students will gain experience with combinatorial constructions, probabilistic analysis, and geometric concepts, and get a glimpse at the active research on how discrete structures behave in the large-scale limit.

Mini cours prévus en février et mars 2026.