Improved analysis of higher order random walks and applications
The motivation of this work is to extend the techniques of higher order random walks on
simplicial complexes to analyze mixing times of Markov chains for combinatorial problems …
simplicial complexes to analyze mixing times of Markov chains for combinatorial problems …
Hypercontractivity on high dimensional expanders
We prove hypercontractive inequalities on high dimensional expanders. As in the settings of
the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities …
the p-biased hypercube, the symmetric group, and the Grassmann scheme, our inequalities …
Local and global expansion in random geometric graphs
Consider a random geometric 2-dimensional simplicial complex X sampled as follows: first,
sample n vectors u 1,…, un uniformly at random on S d− 1; then, for each triple i, j, k∈[n] …
sample n vectors u 1,…, un uniformly at random on S d− 1; then, for each triple i, j, k∈[n] …
New High Dimensional Expanders from Covers
Y Dikstein - Proceedings of the 55th Annual ACM Symposium on …, 2023 - dl.acm.org
We present a new construction of high dimensional expanders based on covering spaces of
simplicial complexes. High dimensional expanders (HDXs) are hypergraph analogues of …
simplicial complexes. High dimensional expanders (HDXs) are hypergraph analogues of …
Coboundary and cosystolic expansion without dependence on dimension or degree
Y Dikstein, I Dinur - arXiv preprint arXiv:2304.01608, 2023 - arxiv.org
We give new bounds on the cosystolic expansion constants of several families of high
dimensional expanders, and the known coboundary expansion constants of order …
dimensional expanders, and the known coboundary expansion constants of order …
From Grassmannian to Simplicial High-Dimensional Expanders
L Golowich - 2023 IEEE 64th Annual Symposium on …, 2023 - ieeexplore.ieee.org
In this paper, we present a new construction of simplicial complexes of subpolynomial
degree with arbitrarily good local spectral expansion. Previously, the only known high …
degree with arbitrarily good local spectral expansion. Previously, the only known high …
Improved product-based high-dimensional expanders
L Golowich - arXiv preprint arXiv:2105.09358, 2021 - arxiv.org
High-dimensional expanders generalize the notion of expander graphs to higher-
dimensional simplicial complexes. In contrast to expander graphs, only a handful of high …
dimensional simplicial complexes. In contrast to expander graphs, only a handful of high …
Local-to-global contraction in simplicial complexes
H Guo, G Mousa - arXiv preprint arXiv:2012.14317, 2020 - arxiv.org
arXiv:2012.14317v2 [cs.DS] 22 Jan 2021 Page 1 arXiv:2012.14317v2 [cs.DS] 22 Jan 2021
LOCAL-TO-GLOBAL CONTRACTION IN SIMPLICIAL COMPLEXES HENG GUO AND GIORGOS …
LOCAL-TO-GLOBAL CONTRACTION IN SIMPLICIAL COMPLEXES HENG GUO AND GIORGOS …
Spectral Independence a New Tool to Analyze Markov Chains
K Liu - 2023 - search.proquest.com
We introduce a versatile technique called spectral independence for the analysis of Markov
chain Monte Carlo algorithms in high-dimensional probability and statistics. We rigorously …
chain Monte Carlo algorithms in high-dimensional probability and statistics. We rigorously …
Sparse High Dimensional Expanders via Local Lifts
High dimensional expanders (HDXs) are a hypergraph generalization of expander graphs.
They are extensively studied in the math and TCS communities due to their many …
They are extensively studied in the math and TCS communities due to their many …