Projects per year
Abstract
We survey results on counting graphs with given degree sequence, focusing on asymptotic results, and mentioning some of the applications of these results. The main recent development is the proof of a conjecture that facilitates access to the degree sequence of a random graph via a model incorporating independent binomial random variables. The basic method used in the proof was to examine the changes in the counting function when the degrees are perturbed. We compare with several previous uses of this type of method.
Original language  English 

Title of host publication  Proceedings of the International Congress of Mathematicians, ICM 2018 
Subtitle of host publication  2018 International Congress of Mathematicians, ICM 2018; Rio de Janeiro; Brazil; 1 August 2018 through 9 August 2018 
Editors  Boyan Sirakov, Paulo Ney de Souza, Marcelo Viana 
Place of Publication  Singapore 
Publisher  World Scientific Publishing 
Pages  32633284 
Number of pages  22 
Volume  4 
ISBN (Electronic)  9789813272934 
DOIs  
Publication status  Published  1 Jan 2018 
Event  International Congress of Mathematicians 2018  Barra da Tijuca, Rio de Janeiro, Brazil Duration: 1 Aug 2018 → 9 Aug 2018 https://icm2018.impa.br/portal/main.html 
Publication series
Name  Proceedings of the International Congress of Mathematicians, ICM 2018 

Volume  4 
Conference
Conference  International Congress of Mathematicians 2018 

Abbreviated title  ICM 2018 
Country/Territory  Brazil 
City  Rio de Janeiro 
Period  1/08/18 → 9/08/18 
Internet address 
Projects
 1 Finished

Advances in the analysis of random structures and their applications: relationships among models
Australian Research Council (ARC)
1/08/12 → 31/12/17
Project: Research