This is an introduction to the mathematical concept of Benjamini-Schramm convergence, which is a type of graph limit theory which works well for sparse graphs. We hope that most of it is understandable by a wide audience with some mathematical background (including some prior exposure to graph theory), but to get the most out of the video it is helpful to know some probability theory and general topology.
Made by: Caio Alves, Aranka Hrušková, and Vilas Winstein.
Music: Jiná Geometrie (Different Geometry), composed by Peter Graham and performed by Aranka Hrušková.
Animations made in Blender and Mathematica (with the MaTeX package). Edited in kdenlive.
References:
Benjamini, I., & Schramm, O. (2011). Recurrence of distributional limits of finite planar graphs.
In Selected Works of Oded Schramm (pp. 533-545). Springer, New York, NY.
Curien, N. (2017). Random Graphs the local convergence point of view
www.imo.universite-paris-sacl...
Lovász, L. (2012). Large networks and graph limits.
Vol. 60. American Mathematical Soc., 2012.
16 июн 2024
