Peaks of random labelings on graphs

• Grant number: 16/18205-6
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate (Direct)
• Start date: January 03, 2017
• End date: July 02, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Serguei Popov
• Grantee: Darcy Gabriel Augusto de Camargo Cunha
• Supervisor: Krzysztof Burdzy
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Washington, United States
• Associated to the scholarship: 13/23081-6 - Percolation and random walks in dependent environments, BP.DD

Abstract

The main goal of this research project is to work with the problem of random labelings on graphs, conditioned to have one or two peaks (i.e. local maximums). More specifically working on the following conjecture: let K_1 and K_2 be respectively the highest and second highest peak of a random labeling on the two dimensional torus with N sites conditioned to have exactly two peaks. Then it is true that N^{-1/2}d(K_1,K_2) goes to 0 as N goes to infinity? The conjecture is that the answer is no. (AU)