BARBOUR, A. D. (1990). Stein’s method for diffusion approximations. Probab. Theory Related Fields 84 297–322. MR1035659 https://doi.org/10.1007/BF01197887
BENTKUS, V. (2005). A Lyapunov type bound in Rd. Theory Probab. Appl. 49 311–323. MR2144310 https://doi.org/10.1137/S0040585X97981123
BHATTACHARYA, R. N. and RANGA RAO, R. (1976). Normal Approximation and Asymptotic Expansions. Wiley Series in Probability and Mathematical Statistics. Wiley, New York. MR0436272
BICKEL, P. J. and BREIMAN, L. (1983). Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test. Ann. Probab. 11 185–214. MR0682809
BOUCHERON, S., LUGOSI, G. and MASSART, P. (2013). Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford Univ. Press, Oxford. With a foreword by Michel Ledoux. MR3185193 https://doi.org/10.1093/acprof:oso/9780199535255.001.0001
CHATTERJEE, S. (2008). A new method of normal approximation. Ann. Probab. 36 1584–1610. MR2435859 https://doi.org/10.1214/07-AOP370
CHATTERJEE, S., DIACONIS, P. and MECKES, E. (2005). Exchangeable pairs and Poisson approximation. Probab. Surv. 2 64–106. MR2121796 https://doi.org/10.1214/154957805100000096
CHATTERJEE, S. and MECKES, E. (2008). Multivariate normal approximation using exchangeable pairs. ALEA Lat. Am. J. Probab. Math. Stat. 4 257–283. MR2453473
CHATTERJEE, S. and SEN, S. (2017). Minimal spanning trees and Stein’s method. Ann. Appl. Probab. 27 1588–1645. MR3678480 https://doi.org/10.1214/16-AAP1239
CHEN, L. H. Y., GOLDSTEIN, L. and SHAO, Q.-M. (2011). Normal Approximation by Stein’s Method. Probability and Its Applications (New York). Springer, Heidelberg. MR2732624 https://doi.org/10.1007/978-3-642-15007-4
DÖBLER, C. and PECCATI, G. (2017). Quantitative de Jong theorems in any dimension. Electron. J. Probab. 22 Paper No. 2, 35. MR3613695 https://doi.org/10.1214/16-EJP19
DUERINCKX, M. (2021). On the size of chaos via Glauber calculus in the classical mean-field dynamics. Comm. Math. Phys. 382 613–653. MR4223483 https://doi.org/10.1007/s00220-021-03978-3
DUNG, N. T. (2019). Explicit rates of convergence in the multivariate CLT for nonlinear statistics. Acta Math. Hungar. 158 173–201. MR3950207 https://doi.org/10.1007/s10474-019-00917-6
FANG, X. and KOIKE, Y. (2020). Large-dimensional central limit theorem with fourth-moment error bounds on convex sets and balls. ArXiv preprint. Available at arXiv:2009.00339.
FANG, X. and KOIKE, Y. (2021). High-dimensional central limit theorems by Stein’s method. Ann. Appl. Probab. 31 1660–1686. MR4312842 https://doi.org/10.1214/20-aap1629
FANG, X. and KOIKE, Y. (2022). New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems. Ann. Appl. Probab. 32 602–631. MR4386537 https://doi.org/10.1214/21-aap1690
GAUNT, R. E. (2016). Rates of convergence in normal approximation under moment conditions via new bounds on solutions of the Stein equation. J. Theoret. Probab. 29 231–247. MR3463084 https://doi.org/10.1007/s10959-014-0562-z
GLORIA, A. and NOLEN, J. (2016). A quantitative central limit theorem for the effective conductance on the discrete torus. Comm. Pure Appl. Math. 69 2304–2348. MR3570480 https://doi.org/10.1002/cpa.21614
GOLDSTEIN, L. and PENROSE, M. D. (2010). Normal approximation for coverage models over binomial point processes. Ann. Appl. Probab. 20 696–721. MR2650046 https://doi.org/10.1214/09-AAP634
GÖTZE, F. (1991). On the rate of convergence in the multivariate CLT. Ann. Probab. 19 724–739. MR1106283
HALL, P. (1988). Introduction to the Theory of Coverage Processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. Wiley, New York. MR0973404 https://doi.org/10.1016/0167-0115(88)90159-0
HUG, D., LAST, G. and SCHULTE, M. (2016). Second-order properties and central limit theorems for geometric functionals of Boolean models. Ann. Appl. Probab. 26 73–135. MR3449314 https://doi.org/10.1214/14-AAP1086
KASPRZAK, M. J. and PECCATI, G. (2023). Supplement to “Vector-valued statistics of binomial processes: Berry–Esseen bounds in the convex distance.” https://doi.org/10.1214/22-AAP1897SUPP
LACHIÈZE-REY, R. and PECCATI, G. (2017). New Berry–Esseen bounds for functionals of binomial point processes. Ann. Appl. Probab. 27 1992–2031. MR3693518 https://doi.org/10.1214/16-AAP1218
LACHIÈZE-REY, R., PECCATI, G. and YANG, X. (2022). Quantitative two-scale stabilization on the Poisson space. Ann. Appl. Probab. 32 3085–3145. MR4474528 https://doi.org/10.1214/21-aap1768
LAST, G. and PENROSE, M. (2018). Lectures on the Poisson Process. Institute of Mathematical Statistics Textbooks 7. Cambridge Univ. Press, Cambridge. MR3791470
LEVINA, E. and BICKEL, P. J. (2005). Maximum likelihood estimation of intrinsic dimension. In Advances in NIPS (K. L. Saul, Y. Weiss and L. Bottou, eds.) 17.
LOTZ, M., MCCOY, M. B., NOURDIN, I., PECCATI, G. and TROPP, J. A. (2020). Concentration of the intrinsic volumes of a convex body. In Geometric Aspects of Functional Analysis. Vol. II. Lecture Notes in Math. 2266 139–167. Springer, Cham. MR4175761 https://doi.org/10.1007/978-3-030-46762-3_6
MECKES, E. (2009). On Stein’s method for multivariate normal approximation. In High Dimensional Probability V: The Luminy Volume. Inst. Math. Stat. (IMS) Collect. 5 153–178. IMS, Beachwood, OH. MR2797946 https://doi.org/10.1214/09-IMSCOLL511
MERIKOSKI, J. K. and VIRTANEN, A. (1997). Bounds for eigenvalues using the trace and determinant. Linear Algebra Appl. 264 101–108. MR1465858 https://doi.org/10.1016/S0024-3795(97)00067-0
MORAN, P. A. P. (1958). Random processes in genetics. Proc. Camb. Philos. Soc. 54 60–71. MR0127989 https://doi.org/10.1017/s0305004100033193
NAZAROV, F. (2003). On the maximal perimeter of a convex set in Rn with respect to a Gaussian measure. In Geometric Aspects of Functional Analysis. (V. D. Milman and G. Schechtman, eds.). Lecture Notes in Math. 1807 169–187. Springer, Berlin. MR2083397 https://doi.org/10.1007/978-3-540-36428-3_15
NOURDIN, I. and PECCATI, G. (2012). Normal Approximations with Malliavin Calculus: From Stein’s Method to Universality. Cambridge Tracts in Mathematics 192. Cambridge Univ. Press, Cambridge. MR2962301 https://doi.org/10.1017/CBO9781139084659
NOURDIN, I., PECCATI, G. and RÉVEILLAC, A. (2010). Multivariate normal approximation using Stein’s method and Malliavin calculus. Ann. Inst. Henri Poincaré Probab. Stat. 46 45–58. MR2641769 https://doi.org/10.1214/08-AIHP308
NOURDIN, I., PECCATI, G. and YANG, X. (2022). Multivariate normal approximation on the Wiener space: New bounds in the convex distance. J. Theoret. Probab. 35 2020–2037. MR4488569 https://doi.org/10.1007/s10959-021-01112-6
PENROSE, M. (2003). Random Geometric Graphs. Oxford Studies in Probability 5. Oxford Univ. Press, Oxford. MR1986198 https://doi.org/10.1093/acprof:oso/9780198506263.001.0001
PENROSE, M. D. and YUKICH, J. E. (2001). Central limit theorems for some graphs in computational geometry. Ann. Appl. Probab. 11 1005–1041. MR1878288 https://doi.org/10.1214/aoap/1015345393
RAIČ, M. (2019). A multivariate Berry–Esseen theorem with explicit constants. Bernoulli 25 2824–2853. MR4003566 https://doi.org/10.3150/18-BEJ1072
REINERT, G. and RÖLLIN, A. (2009). Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition. Ann. Probab. 37 2150–2173. MR2573554 https://doi.org/10.1214/09-AOP467
REINERT, G. and RÖLLIN, A. (2010). Random subgraph counts and U-statistics: Multivariate normal approximation via exchangeable pairs and embedding. J. Appl. Probab. 47 378–393. MR2668495 https://doi.org/10.1239/jap/1276784898
RINOTT, Y. and ROTAR, V. (1996). A multivariate CLT for local dependence with n−1/2 log n rate and applications to multivariate graph related statistics. J. Multivariate Anal. 56 333–350. MR1379533 https://doi.org/10.1006/jmva.1996.0017
RINOTT, Y. and ROTAR, V. (1997). On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics. Ann. Appl. Probab. 7 1080–1105. MR1484798 https://doi.org/10.1214/aoap/1043862425
SANTALÓ, L. A. (2004). Integral Geometry and Geometric Probability, 2nd ed. Cambridge Mathematical Library. Cambridge Univ. Press, Cambridge. With a foreword by Mark Kac. MR2162874 https://doi.org/10.1017/CBO9780511617331
SCHNEIDER, R. and WEIL, W. (2008). Stochastic and Integral Geometry. Probability and Its Applications (New York). Springer, Berlin. MR2455326 https://doi.org/10.1007/978-3-540-78859-1
SCHULTE, M. and YUKICH, J. E. (2019). Multivariate second order Poincaré inequalities for Poisson functionals. Electron. J. Probab. 24 Paper No. 130, 42. MR4040990 https://doi.org/10.1214/19-ejp386
SCHULTE, M. and YUKICH, J. E. (2021). Rates of multivariate normal approximation for statistics in geometric probability. ArXiv preprint.
SHAO, Q.-M. and SU, Z.-G. (2006). The Berry–Esseen bound for character ratios. Proc. Amer. Math. Soc. 134 2153–2159. MR2215787 https://doi.org/10.1090/S0002-9939-05-08177-3
STEELE, J. M. (1986). An Efron–Stein inequality for nonsymmetric statistics. Ann. Statist. 14 753–758. MR0840528 https://doi.org/10.1214/aos/1176349952
