Kesten and Lee [Ann. Appl. Probab. (1996)] proved that the total length of a minimal spanning tree on certain random point configurations in Rd satisfies a central limit theorem. They also raised the question: how to make these results quantitative? Error estimates in central limit theorems satisfied by many other standard functionals studied in stochastic geometry are known, but techniques employed to tackle the problem for those functionals do not apply directly to the minimal spanning tree. Thus, the problem of determining the convergence rate in the central limit theorem for Euclidean minimal spanning trees had remained open. We discuss a general technique for approaching this problem and establish bounds on the convergence rate, thus answering the question of Kesten and Lee. We also discuss a way of quantifying the classical Burton-Keane argument for uniqueness of the infinite open percolation cluster, which plays a crucial role in our approach. Based on joint work with Sourav Chatterjee.
Sanchayan Sen (McGill University, Québec, Canada )
Date & Time
Thu, 17 August 2017, 14:30 to 15:30
Madhava Lecture Hall, ICTS Campus, Bangalore