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10/06/2022
A Toolkit for Robust Thresholds
Consider a host (hyper)graph G which contains a spanning structure due t...
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06/09/2022
Spencer's theorem in nearly input-sparsity time
A celebrated theorem of Spencer states that for every set system S_1,…, ...
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05/03/2022
Optimal minimization of the covariance loss
Let X be a random vector valued in ℝ^m such that X_2≤ 1 almost surely. F...
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11/01/2021
Online Edge Coloring via Tree Recurrences and Correlation Decay
We give an online algorithm that with high probability computes a (e/e-1...
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08/02/2021
Approximate counting and sampling via local central limit theorems
We give an FPTAS for computing the number of matchings of size k in a gr...
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04/14/2021
A Gaussian fixed point random walk
In this note, we design a discrete random walk on the real line which ta...
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01/19/2021
Anticoncentration versus the number of subset sums
Let w⃗ = (w_1,…, w_n) ∈ℝ^n. We show that for any n^-2≤ϵ≤ 1, if #{ξ⃗...
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09/03/2020
On the smoothed analysis of the smallest singular value with discrete noise
Let A be an n× n real matrix, and let M be an n× n random matrix whose e...
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07/13/2020
Perfectly Sampling k≥ (8/3 +o(1))Δ-Colorings in Graphs
We present a randomized algorithm which takes as input an undirected gra...
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06/24/2020
Discrepancy Minimization via a Self-Balancing Walk
We study discrepancy minimization for vectors in ℝ^n under various setti...
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05/18/2020