Abstract: It is common in probability theory and statistics to study distributional convergences of sums of random variables conditioned on another such sum. In this talk I will present a novel approach using Stein’s method for exchangeable pairs that allows to derive conditional central limit theorem of the form $(X_n | Y_n=k)$ with explicit rate of convergence as well as its extensions to multidimensional setting. We will apply these results to particular models including pattern count in a random binary sequence and subgraph count in Erdös-Rényi random graph. This talk is based on joint work with Partha S. Dey https://arxiv.org/abs/2109.09274.
