@inproceedings{5342649150a04af9a43a9fedcb9656dc,
title = "Boolean function analysis on high-dimensional expanders",
abstract = "We initiate the study of Boolean function analysis on high-dimensional expanders. We describe an analog of the Fourier expansion and of the Fourier levels on simplicial complexes, and generalize the FKN theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expanding complex X can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing |X(k)| = O(n) points in comparison to . n k+1 points in the (k + 1)-slice (which consists of all n-bit strings with exactly k + 1 ones).",
keywords = "Boolean Function Analysis, High Dimensional Expanders, Sparse Model",
author = "Yotam Dikstein and Irit Dinur and Yuval Filmus and Prahladh Harsha",
note = "Publisher Copyright: {\textcopyright} 2018 Aditya Bhaskara and Srivatsan Kumar.; 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018 ; Conference date: 20-08-2018 Through 22-08-2018",
year = "2018",
month = aug,
day = "1",
doi = "10.4230/LIPIcs.APPROX-RANDOM.2018.38",
language = "English",
isbn = "9783959770859",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Eric Blais and Rolim, {Jose D. P.} and David Steurer and Klaus Jansen",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018",
address = "Germany",
}