Spectra of ErdösRényi random graphs
Below are histograms of the empirical spectral distribution of adjacency matrices of ErdösRényi random graphs with various average degree. The limit law is purely atomic iff the average degree is smaller than or equal to 1 (see the work of Bordenave Sen and Virag). Simulations are done with 50 matrices of size 5000.
Brownian tree and Brownian excurion
Here are some pictures of uniform planar trees. The embeddings are obtained with GraphViz using a spring algorithm.
Large random maps
Here are some pictures of uniform simple triangulations. The embeddings are again obtained with GraphViz, I'll try to get better pictures when I have the time. If you want to play with these objects, I can provide files of the maps in the .dot format or any reasonable format listing edges and faces.
A uniform simple triangulation with 100 000 faces:



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A uniform simple triangulation with 50 000 faces:



[PNG] [PDF]

A uniform simple triangulation with 10 000 faces:



[PNG] [PDF]
