Las funciones booleans y el lema de Bonami

TL;DR

This paper explores the connection between boolean functions and Bonami's hypercontractivity theorems, emphasizing their applications in social choice theory and discussing key results like FKN, KKL, and the Fourier Entropy/Influence conjecture.

Contribution

It provides an expository analysis of the relationship between boolean functions and hypercontractivity, highlighting significant theorems and conjectures in social choice theory.

Findings

Analysis of the FKN and KKL theorems

Discussion of the Fourier Entropy/Influence conjecture

Clarification of the role of hypercontractivity in social choice

Abstract

In this expository article, we study the relation between the boolean functions and the hypercontractivity theorems of Aline Bonami. We focus on the social choice theory, and present some of the most important results in the area, such as the Friedgut-Kalai-Naor (FKN) and the Kahn-Kalai-Linial (KKL) theorems, and the famous Fourier Entropy/Influence conjecture. -- En este art\'iculo expositivo estudiamos la relaci\'on entre las funciones booleanas y los teoremas de hipercontractividad de Aline Bonami. Nos concentramos en la teor\'ia de la elecci\'on social, y presentamos algunos de los resultados m\'as importantes en el \'area como los teoremas de Friedgut-Kalai-Naor (FKN) y de Kahn-Kalai-Linial (KKL), y la famosa conjetura Entrop\'i{\i}a de Fourier/Influencia.