Asymptotic Combinatorics with Applications in Property Testing and Parameters Estimation.

Abstract

The object of this project is the asymptotic study of combinatorial structures, using techniques such as Szemerédi's Regularity Lemma and limits of convergent graph sequences, with special emphasis on the application of such techniques in the areas of property testing and parameter estimation. The project has as starting point the work on property testing and parameter estimation developed by Alon, Conlon, Fisher, Fox, Krivelevich, Newman, Shapira, among others, which makes use of several variants of the regularity lemma, as well as the theory of convergent sequences of combinatorial structures, developed by Borgs, Chayes, Lovász, Szegedy, among others, which also has consequences in the area of property testing and parameter estimation. We aim at making contributions to the methods and to the applications.