Events

Date: 13 March 2025   Time: 13:00 - 14:00

Location: MB-503

Consider a large random structure -- a stochastic process on the line, a random graph, a random field on the grid -- and a function that depends only on a small part of the structure. Now use a family of transformations to 'move' the domain of the function over the structure, collect each function value, and average. I will present results that show that, under suitable conditions, such transformation averages satisfy a central limit theorem and a Berry-Esseen type bound on the speed of convergence. Several known results for stationary random fields, graphon models of networks, and so forth emerge as special cases. One relevant condition is that the distribution of the random structure remains invariant under the transformations used, which can be read as a probabilistic symmetry property. Loosely speaking: The large-sample theory of i.i.d. averages still holds if the i.i.d. assumption is relaxed to a symmetry assumption.

Joint work with Morgane Austern.