Department of Mathematics, Statistics, and Computer Science, University of Illinois Chicago
Office: SEO 622
Email: visheshj at uic dot edu Accessibility
We are offering a few postdoctoral positions this year. If you are interested in working with me, please consider applying to UIC-RAP and/or UIC-IDEAL and mention my name in your application.
Publications and Preprints
Invertibility of random matrices
Random symmetric matrices: rank distribution and irreducibility of the characteristic polynomial, joint with Asaf Ferber, Ashwin Sah, and Mehtaab Sawhney. To appear in Mathematical Proceedings of the Cambridge Philosophical Society. [arXiv:2106.04049]
On the smallest singular value of symmetric random matrices, joint with Ashwin Sah and Mehtaab Sawhney. To appear in Combinatorics, Probability and Computing. [arXiv:2011.02344]
The smallest singular value of dense random regular digraphs, joint with Ashwin Sah and Mehtaab Sawhney. To appear in International Mathematics Research Notices (IMRN). [arXiv:2008.04755]
Quantitative invertibility of random matrices: a combinatorial perspective. Discrete Analysis, 2021:10. [Journal][arXiv:1908.11255]
Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices. Israel Journal of Mathematics, 242, pp. 461--500 (2021). [Journal][arXiv:1904.10592]
Singularity of random symmetric matrices -- a combinatorial approach to improved bounds, joint with Asaf Ferber. Forum of Mathematics, Sigma, vol. 7, e22, 29 pages (2019). [Journal][arXiv:1809.04718]
Entropic Independence I: Modified Log-Sobolev Inequalities for Fractionally Log-Concave Distributions and High-Temperature Ising Models, joint with Nima Anari, Frederic Koehler, Huy Tuan Pham, and Thuy Duong Vuong. To appear in the 54th ACM Symposium on the Theory of Computing (STOC 2022). [arXiv:2106.04105]
Spectral independence, coupling, and the spectral gap of the Glauber dynamics, joint with Huy Tuan Pham and Thuy Duong Vuong. To appear in Information Processing Letters. [arXiv:2105.01201]
Towards the sampling Lovász Local Lemma, joint with Huy Tuan Pham and Thuy Duong Vuong. To appear in 62nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2021). [arXiv:2011.12196]
Optimal and algorithmic norm regularization of random matrices, joint with Ashwin Sah and Mehtaab Sawhney. To appear in Proceedings of the American Mathematical Society. [arXiv:2012.00175]
On the smoothed analysis of the smallest singular value with discrete noise, joint with Ashwin Sah and Mehtaab Sawhney. To appear in Bulletin of the London Mathematical Society. [arXiv:2009.01699]
On the k-planar local crossing number, joint with John Asplund, Thao Do, and Arran Hamm. Discrete Mathematics, vol. 342, issue 4, pp. 927--933 (2019). [Journal][arXiv:1804.02117]
1-factorizations of pseudorandom graphs, joint with Asaf Ferber. 59th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2018). Random Structures and Algorithms. [Conference][Journal][arXiv:1803.10361]
The probability of selecting k edge-disjoint Hamilton cycles in the complete graph, joint with Asaf Ferber and Kaarel Haenni. Not intended for publication. [arXiv:2001.01149]
Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs, joint with Asaf Ferber. Not intended for publication. [arXiv:1903.12207]
Mean-field approximation
Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective, joint with Frederic Koehler and Andrej Risteski. 51st ACM Symposium on the Theory of Computing (STOC 2019). [Conference][arXiv:1808.07226]
On the number of Hadamard matrices via anti-concentration, joint with Asaf Ferber and Yufei Zhao. To appear in Combinatorics, Probability and Computing. [arXiv:1808.07222]
Universality and least singular values of random product matrices: a simplified approach, joint with Rohit Chaudhuri and Natesh Pillai. Bernoulli, vol. 27, no. 4, pages 2519-2531 (2021). [Journal][arXiv:2007.03595]
A note on the universality of ESDs of inhomogeneous random matrices, joint with Sandeep Silwal. Latin American Journal of Probability and Mathematical Statistics (ALEA), vol. 18, 1047–1059 (2021). [Journal][arXiv:2006.05418]
The strong circular law: a combinatorial view. Random Matrices: Theory and Applications, vol. 10, No. 03, 2150031 (2021). [Journal][arXiv:1904.11108]