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Boolean function analysis on high-dimensional expanders

Irit Dinur, Yotam Dikstein, Yuval Filmus and Prahladh Harsha
Preliminary version in RANDOM'18

We initiate the study of Boolean function analysis on high-dimensional expanders, and more generally, on weighted simplicial complexes.

We identify a linear-algebraic condition under which there is a notion of Fourier expansion for functions on the facets of the complex, a notion similar to the unique harmonic multilinear expansion for functions on the slice or Johnson scheme, and sharing many of its properties.

We prove a rudimentary FKN theorem for high-dimensional expanders, utilizing a recent agreement theorem of Dinur and Kaufman.

Our work also gives a novel definition of high-dimensional expansion. We also generalize this notion (work in progress) to the Grassmann scheme.

BibTeX

@inproceedings{DDFH2018,
 author = {Yotam Dikstein and Irit Dinur and Yuval Filmus and Prahladh Harsha},
 title = {Boolean function analysis on high-dimensional expanders},
 booktitle = {22nd International Conference on Randomization and Computation (RANDOM'2018)},
 year = {2018}
}
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