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Graphons and graphexes as limits of sparse graphs - lecture 2
Post-edited
Authors : Borgs, Christian (Author of the conference)
CIRM (Publisher )
05C60 - Isomorphism problems (reconstruction conjecture, perfect graphs, etc.)
05C80 - Random graphs
60F10 - Large deviations
82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
CIRM (Publisher )
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| left convergence for dense graphs sampling convergence for sparse graphs Poisson sampling graphon process random measure graphex configuration model |
Abstract :
Graphons and graphexes are limits of graphs which allow us to model and estimate properties of large-scale networks. In this pair of talks, we review the theory of dense graph limits, and give two alterative theories for limits of sparse graphs – one leading to unbounded graphons over probability spaces, and the other leading to bounded graphons (and graphexes) over sigma-finite measure spaces. Talk I, given by Jennifer, will review the general theory, highlight the unbounded graphons, and show how they can be used to consistently estimate properties of large sparse networks. This talk will also give an application of these sparse graphons to collaborative filtering on sparse bipartite networks. Talk II, given by Christian, will recast limits of dense graphs in terms of exchangeability and the Aldous Hoover Theorem, and generalize this to obtain sparse graphons and graphexes as limits of subgraph samples from sparse graph sequences. This will provide a dual view of sparse graph limits as processes and random measures, an approach which allows a generalization of many of the well-known results and techniques for dense graph sequences.
Keywords : sparse graphs; graphex; dense exchangeable graphs; graphon; network data; Aldous Hoover theorem
MSC Codes : Keywords : sparse graphs; graphex; dense exchangeable graphs; graphon; network data; Aldous Hoover theorem
05C60 - Isomorphism problems (reconstruction conjecture, perfect graphs, etc.)
05C80 - Random graphs
60F10 - Large deviations
82B20 - Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 11/09/2018 Conference Date : 28/08/2018 Subseries : Research talks arXiv category : Statistics Theory ; Combinatorics ; Probability Mathematical Area(s) : Combinatorics Format : MP4 (.mp4) - HD Video Time : 00:42:11 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-08-28_Borgs.mp4 
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Information on the Event
Event Title : Advances in Statistical Mechanics / Avancées en mécanique statistiqueEvent Organizers : Arguin, Louis-Pierre ; Gayrard, Véronique ; Kistler, Nicola ; Kourkova, Irina Dates : 27/08/2018 - 31/08/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1855.html
Citation Data
DOI : 10.24350/CIRM.V.19442603Cite this video as: Borgs, Christian (2018). Graphons and graphexes as limits of sparse graphs - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19442603 URI : http://dx.doi.org/10.24350/CIRM.V.19442603 |
See Also
- [Post-edited] Graphons and graphexes as limits of sparse graphs - lecture 1 / Author of the conference Chayes, Jennifer Tour.
- [Multi angle] Space-time covariance of KPZ growth models / Author of the conference Ferrari, Patrik.
- [Multi angle] Remarks on the Riemann hypothesis / Author of the conference Newman, Charles.
- [Multi angle] Geometric description of the spherical Spin-Glass Gibbs measures and temperature chaos / Author of the conference Ben Arous, Gérard.
Bibliography
