Mathematical Research Letters
Volume 22 (2015)
Higher dimensional distortion of random complexes
Pages: 1295 – 1316
Using the random complexes of Linial and Meshulam [N. Linial and R. Meshulam, “Homological connectivity of random 2-complexes” Combinatorica, 26 (2006), pp. 475–487], we exhibit a large family of simplicial complexes for which, whenever affinely embedded into Euclidean space, the filling areas of simplicial cycles is greatly distorted. This phenomenon can be regarded as a higher order analogue of the metric distortion of embeddings of random graphs.