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Peaks of random labelings on graphs

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


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.