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Asymptotic freeness of large graphs with large degree Male, Camille
Description
Let $A_1,\dots,A_L$ be adjacency matrices of independent random graphs $G_1,\dots,G_L$ on the vertex set $\{1,...,N\}$. Assume for each $\ell=1,\dots,L$ that the expected degree of a vertex of $G_\ell$ uniformly chosen at random goes to infinity, and that each graph is invariant in law by relabelling of its vertices. We state a quantitative estimate of decorrelation on the edges of the graphs that implies the asymptotic freeness of well-normalized versions of $A_1,\dots,A_L$, as well as their asymptotic freeness with arbitrary matrices. We prove that this estimate holds for the uniform simple $d_N$-regular graph with $|d_N-\frac N 2|$ going to infinity fast enough. The proof is based on asymptotic traffic independence and combinatorial manipulations.
Item Metadata
Title |
Asymptotic freeness of large graphs with large degree
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-12-06T10:27
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Description |
Let $A_1,\dots,A_L$ be adjacency matrices of independent random graphs $G_1,\dots,G_L$ on the vertex set $\{1,...,N\}$. Assume for each $\ell=1,\dots,L$ that the expected degree of a vertex of $G_\ell$ uniformly chosen at random goes to infinity, and that each graph is invariant in law by relabelling of its vertices. We state a quantitative estimate of decorrelation on the edges of the graphs that implies the asymptotic freeness of well-normalized versions of $A_1,\dots,A_L$, as well as their asymptotic freeness with arbitrary matrices. We prove that this estimate holds for the uniform simple $d_N$-regular graph with $|d_N-\frac N 2|$ going to infinity fast enough. The proof is based on asymptotic traffic independence and combinatorial manipulations.
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Extent |
55 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Université Bordeaux & CNRS
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Series | |
Date Available |
2017-05-15
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0347458
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International