---
_id: '15063'
abstract:
- lang: eng
  text: We consider the least singular value of a large random matrix with real or
    complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal
    lower tail estimate on this singular value in the critical regime where z is around
    the spectral edge, thus improving the classical bound of Sankar, Spielman and
    Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation
    in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on
    the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).
acknowledgement: Partially supported by ERC Advanced Grant No. 338804. This project
  has received funding from the European Union’s Horizon 2020 research and innovation
  programme under the Marie Sklodowska-Curie Grant Agreement No. 66538
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
  full_name: Cipolloni, Giorgio
  id: 42198EFA-F248-11E8-B48F-1D18A9856A87
  last_name: Cipolloni
  orcid: 0000-0002-4901-7992
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Dominik J
  full_name: Schröder, Dominik J
  id: 408ED176-F248-11E8-B48F-1D18A9856A87
  last_name: Schröder
  orcid: 0000-0002-2904-1856
citation:
  ama: Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular
    value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>.
    2020;1(1):101-146. doi:<a href="https://doi.org/10.2140/pmp.2020.1.101">10.2140/pmp.2020.1.101</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2020). Optimal lower bound
    on the least singular value of the shifted Ginibre ensemble. <i>Probability and
    Mathematical Physics</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/pmp.2020.1.101">https://doi.org/10.2140/pmp.2020.1.101</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower
    Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability
    and Mathematical Physics</i>. Mathematical Sciences Publishers, 2020. <a href="https://doi.org/10.2140/pmp.2020.1.101">https://doi.org/10.2140/pmp.2020.1.101</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least
    singular value of the shifted Ginibre ensemble,” <i>Probability and Mathematical
    Physics</i>, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least
    singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics.
    1(1), 101–146.
  mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value
    of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>,
    vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:<a href="https://doi.org/10.2140/pmp.2020.1.101">10.2140/pmp.2020.1.101</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics
    1 (2020) 101–146.
date_created: 2024-03-04T10:27:57Z
date_published: 2020-11-16T00:00:00Z
date_updated: 2024-03-04T10:33:15Z
day: '16'
department:
- _id: LaEr
doi: 10.2140/pmp.2020.1.101
ec_funded: 1
external_id:
  arxiv:
  - '1908.01653'
intvolume: '         1'
issue: '1'
keyword:
- General Medicine
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1908.01653
month: '11'
oa: 1
oa_version: Preprint
page: 101-146
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
publication: Probability and Mathematical Physics
publication_identifier:
  issn:
  - 2690-1005
  - 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal lower bound on the least singular value of the shifted Ginibre ensemble
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2020'
...