The Annals of Probability
- Ann. Probab.
- Volume 38, Number 6 (2010), 2443-2485.
Applications of Stein’s method for concentration inequalities
Stein’s method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie–Weiss model at critical temperature (where it obeys a nonstandard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymptotics for the number of triangles in the Erdős–Rényi random graph G(n, p) when p ≥ 0.31. Similar results are derived also for general subgraph counts. (3) We obtain some interesting concentration inequalities for the Ising model on lattices that hold at all temperatures.
Ann. Probab., Volume 38, Number 6 (2010), 2443-2485.
First available in Project Euclid: 24 September 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E15: Inequalities; stochastic orderings 60F10: Large deviations
Secondary: 60C05: Combinatorial probability 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Chatterjee, Sourav; Dey, Partha S. Applications of Stein’s method for concentration inequalities. Ann. Probab. 38 (2010), no. 6, 2443--2485. doi:10.1214/10-AOP542. https://projecteuclid.org/euclid.aop/1285334211