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Entropic CLT and phase transition in high-dimensional Wishart matrices
TLDR
We prove an information theoretic phase transition: such matrices are close in total variation distance to the corresponding Gaussian ensemble if and only if $d$ is much larger than $n^3$. Expand
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Recovery and Rigidity in a Regular Stochastic Block Model
TLDR
We introduce a variant of the binary model which we call the regular stochastic block model (RSBM). Expand
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Consistent nonparametric estimation for heavy-tailed sparse graphs
We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms andExpand
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Upper tails and independence polynomials in random graphs
Abstract The upper tail problem in the Erdős–Renyi random graph G ∼ G n , p asks to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ .Expand
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Upper Tail Large Deviations for Arithmetic Progressions in a Random Set
Let $X_k$ denote the number of $k$-term arithmetic progressions in a random subset of $\mathbb{Z}/N\mathbb{Z}$ or $\{1, \dots, N\}$ where every element is included independently with probability $p$.Expand
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A complete characterization of the evolution of RC4 pseudo random generation algorithm
TLDR
We provide a complete characterization of the RC4 Pseudo Random Generation Algorithm (PRGA) for one step: i = i + 1; j = j + S[i]; swap(S[i], S[j]); z = S[S[J] + S [j]]. Expand
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Cutoff for the East Process
The East process is a 1d kinetically constrained interacting particle system, introduced in the physics literature in the early 1990s to model liquid-glass transitions. Spectral gap estimates ofExpand
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High-girth near-Ramanujan graphs with localized eigenvectors
We show that for every prime $d$ and $\alpha\in (0,1/6)$, there is an infinite sequence of $(d+1)$-regular graphs $G=(V,E)$ with girth at least $2\alpha \log_{d}(|V|)(1-o_d(1))$, second adjacencyExpand
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Upper Tails for Edge Eigenvalues of Random Graphs
TLDR
In this note we prove a precise large deviation principle for the largest and second largest eigenvalues of a sparse Erd\H{o}s-R\'enyi graph. Expand
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On Non-localization of Eigenvectors of High Girth Graphs
TLDR
We prove improved bounds on how localized an eigenvector of a high girth regular graph can be, and present examples showing that these bounds are close to sharp. Expand
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