3 papers
math.CO2020
Algebraic and combinatorial expansion in random simplicial complexes
Nikolaos Fountoulakis, Michał Przykucki
In this paper we consider the expansion properties and the spectrum of the combinatorial Laplace operator of a -dimensional Linial-Meshulam random simplicial complex, above the…
math.PR2019
High-dimensional bootstrap processes in evolving simplicial complexes
Nikolaos Fountoulakis, Michał Przykucki
We study bootstrap percolation processes on random simplicial complexes of some fixed dimension . Starting from a single simplex of dimension , we build our complex dy…
math.CO2019
Shotgun reconstruction in the hypercube
Michał Przykucki, Alexander Roberts, Alex Scott
Mossel and Ross raised the question of when a random colouring of a graph can be reconstructed from local information, namely the colourings (with multiplicity) of balls of given r…