Figure A chord diagram with n chords sampled with weight q per crossing with in this case n=2000 and q=0.95. The right image shows a planar map realization of the chord diagram with the same boundary metric.Figure Random chord diagrams with n=1500 chords and q=0.9, 0.95, 0.98, 0.99, together with planar map realizations.Figure Random chord diagrams with n=2000 chords and q=0.95, 0.98, 0.99, together with planar map realizations.Figure Planar map realizations of random chord diagrams with n(1-q)=64 fixed and n = 256, 512, 1024, 2048.Figure Planar map realizations of random chord diagrams with n(1-q)=16 fixed and n = 100, ..., 2400.Figure Planar map realizations of random chord diagrams with n(1-q)=-16 fixed and n = 32, ..., 512.Video A planar map realization for n=1000 chords and q=0.96.Video A planar map realization for n=3000 chords and q=0.9.
References
[1] Berkooz, Micha, Mikhail Isachenkov, Vladimir Narovlansky, and Genis Torrents. Towards a full solution of the large N double-scaled SYK model. Journal of High Energy Physics 2019, no. 3 (2019): 1-72.
[2] Berkooz, Micha, and Ohad Mamroud. A cordial introduction to double scaled SYK. Reports on Progress in Physics 88, no. 3 (2025): 036001.
[3] Budd, Timothy. Double-scaled SYK from boundary metrics of planar maps. arXiv preprint arXiv:2607.01995 (2026).
