{"date_updated":"2026-06-29T09:19:14Z","acknowledgement":"Z.H. was supported by SNSF grant 200021-228014. M.K. was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. L.S. was supported by the Deutsche Forschungsgemeinschaft (DFG, German\r\nResearch Foundation)—CRC 1720–539309657. This research was conducted during the period M.S. served\r\nas a Clay Research Fellow. This work began when the authors were visiting Mathematisches Forschungsinstitut Oberwolfach, which\r\nprovided ideal working conditions. M.S. thanks Vishesh Jain for initial discussions regarding the problem.\r\nWe also thank the anonymous referee for helpful comments.","issue":"12","citation":{"ieee":"Z. Hunter, M. A. Kwan, L. Sauermann, and M. Sawhney, “On random matrices with large corank,” <i>International Mathematics Research Notices</i>, vol. 2026, no. 12. Oxford University Press, 2026.","chicago":"Hunter, Zach, Matthew Alan Kwan, Lisa Sauermann, and Mehtaab Sawhney. “On Random Matrices with Large Corank.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2026. <a href=\"https://doi.org/10.1093/imrn/rnag126\">https://doi.org/10.1093/imrn/rnag126</a>.","ista":"Hunter Z, Kwan MA, Sauermann L, Sawhney M. 2026. On random matrices with large corank. International Mathematics Research Notices. 2026(12), rnag126.","ama":"Hunter Z, Kwan MA, Sauermann L, Sawhney M. On random matrices with large corank. <i>International Mathematics Research Notices</i>. 2026;2026(12). doi:<a href=\"https://doi.org/10.1093/imrn/rnag126\">10.1093/imrn/rnag126</a>","apa":"Hunter, Z., Kwan, M. A., Sauermann, L., &#38; Sawhney, M. (2026). On random matrices with large corank. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnag126\">https://doi.org/10.1093/imrn/rnag126</a>","short":"Z. Hunter, M.A. Kwan, L. Sauermann, M. Sawhney, International Mathematics Research Notices 2026 (2026).","mla":"Hunter, Zach, et al. “On Random Matrices with Large Corank.” <i>International Mathematics Research Notices</i>, vol. 2026, no. 12, rnag126, Oxford University Press, 2026, doi:<a href=\"https://doi.org/10.1093/imrn/rnag126\">10.1093/imrn/rnag126</a>."},"status":"public","_id":"22147","author":[{"first_name":"Zach","full_name":"Hunter, Zach","last_name":"Hunter"},{"first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567"},{"last_name":"Sauermann","full_name":"Sauermann, Lisa","first_name":"Lisa"},{"first_name":"Mehtaab","full_name":"Sawhney, Mehtaab","last_name":"Sawhney"}],"date_published":"2026-06-01T00:00:00Z","article_type":"original","title":"On random matrices with large corank","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnag126","researchdata_availability":"no","month":"06","supplementarymaterial":"no","das_tickbox":"0","department":[{"_id":"MaKw"}],"ddc":["500"],"publication_status":"published","year":"2026","oa_version":"Published Version","oa":1,"volume":2026,"has_accepted_license":"1","quality_controlled":"1","file":[{"file_size":524993,"date_created":"2026-06-29T09:15:15Z","content_type":"application/pdf","checksum":"396b47d0532d7ea509f8cd30f11392a8","success":1,"access_level":"open_access","relation":"main_file","date_updated":"2026-06-29T09:15:15Z","creator":"dernst","file_id":"22151","file_name":"2026_IMRN_Hunter.pdf"}],"OA_type":"hybrid","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","PlanS_conform":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"      2026","publication":"International Mathematics Research Notices","arxiv":1,"license":"https://creativecommons.org/licenses/by/4.0/","file_date_updated":"2026-06-29T09:15:15Z","fulldoi":"https://doi.org/10.1093/imrn/rnag126","external_id":{"arxiv":["2510.12933"]},"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"scopus_import":"1","type":"journal_article","abstract":[{"text":"Let 1 ≤ k ≤ n and M be a random n × n matrix with independent uniformly random {±1}-entries. We\r\nshow that there exists an absolute constant c > 0 such that\r\nP[rank(M) ≤ n − k] ≤ exp(−cnk).\r\nThis confirms a well-known prediction in the area, extending a result of Rudelson (who previously\r\nproved this same result under the restriction k ≤ √n, via different methods).","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","article_number":"rnag126","date_created":"2026-06-28T22:01:35Z","OA_place":"publisher","publisher":"Oxford University Press","project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"}]}