Sean O'Rourke : Publications

A full list of my papers and preprints is available below. Many of my recent preprints can also be found at the arXiv in list format.

• Marcus Michelen and Sean O'Rourke, On random polynomials with an intermediate number of real roots, submitted, available at arXiv:2310.16966, 2023.
• Sean O'Rourke, Zhi Yin, and Ping Zhong, Spectrum of Laplacian matrices associated with large random elliptic matrices, submitted, available at arXiv:2308.16171, 2023.
• Andrew Campbell, Sean O'Rourke, and David Renfrew, The fractional free convolution of $R$-diagonal operators and random polynomials under repeated differentiation, submitted, available at arXiv:2307.11935, 2023.
• Sean O'Rourke, Van Vu, and Ke Wang, Optimal Subspace Perturbation Bounds under Gaussian Noise, 2023 IEEE International Symposium on Information Theory (ISIT), Taipei, Taiwan, 2023, pp. 2601--2606.
• Andrew Campbell, Kyle Luh, and Sean O'Rourke (with an appendix by Santiago Arenas-Velilla and Victor Pérez-Abreu), Extreme eigenvalues of Laplacian random matrices with Gaussian entries, available at arXiv:2211.17175, 2022.
• Andrew Campbell and Sean O'Rourke, Spectrum of Lévy-Khintchine Random Laplacian Matrices, Journal of Theoretical Probability, to appear.
• Isabelle Kraus, Marcus Michelen, and Sean O'Rourke, Sums of random polynomials with differing degrees, Transactions of the American Mathematical Society, to appear.
• Sean O'Rourke and Philip Matchett Wood, Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations, Linear Algebra and its Applications, Volume 657 (2023), 50--126.
• Richard Border, Sean O'Rourke, Teresa de Candia, Michael E. Goddard, Peter M. Visscher, Loic Yengo, Mathew Jones, and Matthew C. Keller, Assortative Mating Biases Marker-based Heritability Estimators, Nature Communications 13, 660 (2022).
• A. Campbell, S. O'Rourke, Spectrum of Heavy-Tailed Elliptic Random Matrices, Electronic Journal of Probability, Vol. 27 (2022), Paper No. 125, 56 pp.
• V. Jain, I. Jana, K. Luh, S. O'Rourke, Circular law for random block band matrices with genuinely sublinear bandwidth, Journal of Mathematical Physics, Vol. 62, No. 8, Paper No. 083306 (2021).
• K. Luh, S. O'Rourke, Eigenvectors and controllability of non-Hermitian random matrices and directed graphs, Electronic Journal of Probability, Vol. 26, Paper No. 16, 1--43 (2021).
• S. O'Rourke, N. Williams, Partial linear eigenvalue statistics for non-Hermitian random matrices, Theory of Probability and its Applications, 67 (2023), no. 4, 613--632.
• S. O'Rourke, S. Steinerberger, A Nonlocal Transport Equation Modeling Complex Roots of Polynomials under Differentiation, Proceedings of the American Mathematical Society, Vol. 149, No. 4, 1581--1592 (2021).
• S. O'Rourke, T. R. Reddy, Sums of random polynomials with independent roots, Journal of Mathematical Analysis and Applications, Vol. 495, No. 1 (2021), 124719.
• S. O'Rourke, N. Williams, On the local pairing behavior of critical points and roots of random polynomials, Electronic Journal of Probability, Vol. 25, Paper No. 100 (2020), 68 pp.
• K. Luh, S. O'Rourke, Eigenvector Delocalization for Non-Hermitian Random Matrices and Applications, Random Structures & Algorithms, Vol. 57, No. 1 (2020), 169--210.
• N. Coston, S. O'Rourke, Gaussian fluctuations for linear eigenvalue statistics of products of independent iid random matrices, Journal of Theoretical Probability, Vol. 33, No. 3 (2020), 1541--1612.
• S. O'Rourke, V. Vu, K. Wang, Matrices with Gaussian Noise: Optimal Estimates for Singular Subspace Perturbation, IEEE Transactions on Information Theory, to appear.
• P. Kopel, S. O'Rourke, V. Vu, Random matrix products: Universality and least singular values, Annals of Probability, Vol. 48, No. 3 (2020), 1372--1410.
• N. Coston, S. O'Rourke, P. Wood, Outliers in the spectrum for products of independent random matrices, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 56, No. 2 (2020), 1284--1320.
• S. O'Rourke, B. Touri, Littlewood-Offord theory and controllability of random structures, 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, 2016, pp. 5195--5200.
• S. O'Rourke, N. Williams, Pairing between zeros and critical points of random polynomials with independent roots, Transactions of the American Mathematical Society, Volume 371, Number 4 (2019), pp. 2343--2381.
• S. O'Rourke, P. Wood, Low-degree factors of random polynomials, Journal of Theoretical Probability, Volume 32, Issue 2 (2019), pp. 1076--1104.
• S. O'Rourke, V. Vu, K. Wang, Eigenvectors of random matrices: A survey, Journal of Combinatorial Theory, Series A, Vol. 144 (2016), 361--442.
• S. O'Rourke, B. Touri, On a conjecture of Godsil concerning controllable random graphs, SIAM J. Control Optim. Vol. 54, No. 6 (2016), pp. 3347--3378.
• S. O'Rourke, P. Wood, Spectra of nearly Hermitian random matrices, Annales de l’Institut Henri Poincaré - Probabilités et Statistiques, Vol. 53, No. 3 (2017), 1241--1279.
• S. O'Rourke, B. Touri, Controllability of random systems: Universality and minimal controllability, available at arXiv:1506.03125.
• S. O'Rourke, Critical points of random polynomials and characteristic polynomials of random matrices, International Mathematics Research Notices, Vol. 2016, No. 18 (2016), pp. 5616--5651.
• S. O'Rourke, D. Renfrew, Central limit theorem for linear eigenvalue statistics of elliptic random matrices, Journal of Theoretical Probability, Volume 29, Issue 3 (2016), pp. 1121--1191.
• S. O'Rourke, D. Renfrew, A. Soshnikov, V. Vu, Products of independent elliptic random matrices, J. Stat. Phys. Vol. 160, No. 1 (2015), 89--119.
• S. O'Rourke, V. Vu, K. Wang, Random perturbation of low rank matrices: Improving classical bounds, Linear Algebra and its Applications, Volume 540 (2018), pp. 26--59.
• S. O'Rourke, D. Renfrew, Low rank perturbations of large elliptic random matrices, Electronic Journal of Probability Vol. 19, No. 43, 1--65 (2014).
• H. Nguyen, S. O'Rourke, On the concentration of random multilinear forms and the universality of random block matrices, Probability Theory and Related Fields Volume 162, Issue 1-2, pp 97--154 (2015).
• S. O'Rourke, V. Vu, Universality of local eigenvalue statistics in random matrices with external source, Random Matrices: Theory and Applications, Vol. 3, No. 2 (2014).
• S. O'Rourke, A. Soshnikov, Partial linear eigenvalue statistics for Wigner and sample covariance random matrices, J. Theor. Probab. Vol. 28, No. 2 (2015), 726--744.
• H. Nguyen, S. O'Rourke, The elliptic law, International Mathematics Research Notices, Vol. 2015, No. 17 (2015), pp. 7620--7689.
• S. O'Rourke, A note on the Marchenko-Pastur law for a class of random matrices with dependent entries, Electronic Communications in Probability, Vol. 17, Art. 28, pp. 1--13 (2012).
• S. O'Rourke, Fluctuations of Matrix Entries of Analytic Functions of Non-Hermitian Random Matrices, Random Matrices: Theory and Applications, Vol. 1, No. 3 (2012).
• S. O'Rourke, D. Renfrew, A. Soshnikov, Fluctuations of Matrix Entries of Regular Functions of Sample Covariance Random Matrices, Theory Probab. Appl. Vol. 58, No. 4, pp. 615--639 (2014).
• S. O'Rourke, D. Renfrew, A. Soshnikov, On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries, J. Theor. Probab. Vol. 26, No. 3 (2013), 750--780.
• S. O'Rourke, A. Soshnikov, Products of Independent Non-Hermitian Random Matrices, Electronic Journal of Probability, Vol. 16, Art. 81, 2219--2245 (2011).
• P. Dueck, S. O'Rourke, D. Renfrew, A. Soshnikov, Spectral Properties of Large Random Matrices with Independent Entries, Noncommutative Harmonic Analysis with Applications to Probability III. Banach Center Publ. Vol. 96, 115--134 (2012).
• S. O'Rourke, Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices, J. Stat. Phys. Vol. 138, No. 6 (2010), 1045--1066.