Basic Results of Large deviations theory and application to the Curie-Weiss spin model

• Grant number: 24/01165-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2024
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Alexsandro Giacomo Grimbert Gallo
• Grantee: Felipe Luis Giacomini
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The main objective of the project is to illustrate the relation that exists betweenthe large deviation theory and statistical physics, notably through the proof ofthe phase transition phenomenon for the Curie Weiss spin model in mean field.It will be an oportunity to make a careful study of the basic theory of largedeviation, through Cramér's theorem and possibly Sanov's theorem. This willcomplement the probabilistic culture of the candidate, currently studying in theundergraduate course of statistics.