Spectral clustering in the Gaussian mixture block model
S Li, T Schramm - arXiv preprint arXiv:2305.00979, 2023 - arxiv.org
Gaussian mixture block models are distributions over graphs that strive to model modern
networks: to generate a graph from such a model, we associate each vertex $ i $ with a …
networks: to generate a graph from such a model, we associate each vertex $ i $ with a …
[PDF][PDF] On The Fourier Coefficients of High-Dimensional Random Geometric Graphs
K Bangachev, G Bresler - Proceedings of the 56th Annual ACM …, 2024 - dl.acm.org
The random geometric graph RGG (n, S d− 1, p) is formed by sampling n iid vectors {V i} i= 1
n uniformly on S d− 1 and placing an edge between pairs of vertices i and j for which⟨ V i, V …
n uniformly on S d− 1 and placing an edge between pairs of vertices i and j for which⟨ V i, V …
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 …
Random Algebraic Graphs and Their Convergence to ErdőS–Rényi
K Bangachev, G Bresler - Random Structures & Algorithms, 2025 - Wiley Online Library
ABSTRACT A random algebraic graph is defined by a group 𝒢 with a uniform distribution
over it and a connection σ: 𝒢→ 0, 1 with expectation p, p, satisfying σ (g)= σ (g− 1) σ (g) …
over it and a connection σ: 𝒢→ 0, 1 with expectation p, p, satisfying σ (g)= σ (g− 1) σ (g) …
Guarantees for spontaneous synchronization on random geometric graphs
P Abdalla, AS Bandeira, C Invernizzi - SIAM Journal on Applied Dynamical …, 2024 - SIAM
The Kuramoto model is a classical mathematical model in the field of nonlinear dynamical
systems that describes the evolution of coupled oscillators in a network that may reach a …
systems that describes the evolution of coupled oscillators in a network that may reach a …
Sandwiching Random Geometric Graphs and Erdos-Renyi with Applications: Sharp Thresholds, Robust Testing, and Enumeration
K Bangachev, G Bresler - arXiv preprint arXiv:2408.00995, 2024 - arxiv.org
The distribution $\mathsf {RGG}(n,\mathbb {S}^{d-1}, p) $ is formed by sampling
independent vectors $\{V_i\} _ {i= 1}^ n $ uniformly on $\mathbb {S}^{d-1} $ and placing an …
independent vectors $\{V_i\} _ {i= 1}^ n $ uniformly on $\mathbb {S}^{d-1} $ and placing an …
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 …
Sparser Abelian High Dimensional Expanders
Y Dikstein, S Liu, A Wigderson - arXiv preprint arXiv:2411.08839, 2024 - arxiv.org
We present two new explicit constructions of Cayley high dimensional expanders (HDXs)
over the abelian group $\mathbb {F} _2^ n $. Our expansion proofs use only linear algebra …
over the abelian group $\mathbb {F} _2^ n $. Our expansion proofs use only linear algebra …
Sparse High Dimensional Expanders via Local Lifts
I Ben Yaacov, Y Dikstein, G Maor - … Optimization. Algorithms and …, 2024 - drops.dagstuhl.de
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 …
[图书][B] Geometry of Local-spectral Expanders
S Liu - 2023 - search.proquest.com
Expanders are well-connected graphs. They have numerous applications in constructions of
error correcting codes, metric embedding, derandomization, sampling algorithms, etc. Local …
error correcting codes, metric embedding, derandomization, sampling algorithms, etc. Local …