This paper is a short exposition of Stein’s method normal approximation from my personal perspective. It focuses mainly on the characterization distribution and construction Stein identities. Through examples, it provides glimpses into many approaches to constructing identities diverse applications mathematical problems. also includes anecdotes historical interest, including how discovered his ...

Abstract In this paper, a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs. This does not rely on the concentration inequalities developed Chen Shao [4,5] can be applied quadratic forms general Curie-Weiss model.

To lower bound the effective dimension for local Hamiltonian models, we will use a theorem from [1, 2] as a stepping stone. This is a quantum version of the BerryEsseen theorem. The Berry-Esseen theorem is a more powerful statement than the central limit theorem, as it gives the rate of convergence of a distribution to a Gaussian. Let H = ∑ ν Eν |ν〉〈ν| be k-local, i.e., let H be of the form H =...

Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...