Raphael Ducatez

activity

20162023

most citedFull large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices

3 citations · 10 across the 10 of their papers we have counts for

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7 papers · 1 filter

math.PR2023

Spectral gap and embedded trees for the Laplacian of the Erdős-Rényi graph

Raphael Ducatez, Renaud Rivier

For the Erdős-Rényi graph of size $N$ with mean degree $(1 + o (1)) \frac{l o g N}{t + 1} \leq d \leq (1 - o (1)) \frac{l o g N}{t}$ where $t \in N^{*}$ , with high probability the smallest…

math.PR2023★ 2 cited

Localized phase for the Erdős-Rényi graph

Johannes Alt, Raphael Ducatez, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph $G (N, d / N)$ for $lo g N ≪ d ≲ lo g N$ . We show the existence of a localized phas…

math.PR2023★ 3 cited

Full large deviation principles for the largest eigenvalue of sub-Gaussian Wigner matrices

Nicholas A. Cook, Raphael Ducatez, Alice Guionnet

We establish precise upper-tail asymptotics and large deviation principles for the rightmost eigenvalue $λ_{1}$ of Wigner matrices with sub-Gaussian entries. In contrast to the case…

math.PR2021

The completely delocalized region of the Erdős-Rényi graph

Johannes Alt, Raphael Ducatez, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of the Erdős-Rényi graph on $N$ vertices with edge probability $\frac{d}{N}$ . We determine the full region of delocalization by…

math.PR2021★ 2 cited

Poisson statistics and localization at the spectral edge of sparse Erdős-Rényi graphs

Johannes Alt, Raphael Ducatez, Antti Knowles

We consider the adjacency matrix $A$ of the Erdős-Rényi graph on $N$ vertices with edge probability $d / N$ . For $(lo g lo g N)^{4} ≪ d ≲ lo g N$ , we prove that the eigenvalue…

math.PR2020

Delocalization transition for critical Erdős-Rényi graphs

Johannes Alt, Raphael Ducatez, Antti Knowles

We analyse the eigenvectors of the adjacency matrix of a critical Erdős-Rényi graph $G (N, d / N)$ , where $d$ is of order $lo g N$ . We show that its spectrum splits into two ph…

math.PR2019

Extremal eigenvalues of critical Erdős-Rényi graphs

Johannes Alt, Raphaël Ducatez, Antti Knowles

We complete the analysis of the extremal eigenvalues of the the adjacency matrix $A$ of the Erdős-Rényi graph $G (N, d / N)$ in the critical regime $d ≍ lo g N$ of the transition…