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• 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