{"title":"Repeated Erfc Statistics for Deformed GinUEs","authors":"Dang-Zheng Liu, Lu Zhang","doi":"10.1007/s00023-025-01561-3","DOIUrl":null,"url":null,"abstract":"<div><p>For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix <span>\\(X_0\\)</span>, under certain assumption on <span>\\(X_0\\)</span>, we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE statistics and critical statistics, which, respectively, correspond to regular and quadratic vanishing spectral points. As a continuation of our previous study on critical statistics (Liu and Zhang in Critical edge statistics for deformed GinUEs. Preprint arXiv: 2311.13227), in this paper we establish the local statistics of GinUE type at the regular spectral edge, which is characterized by a repeated erfc integral found in Liu and Zhang (Probab Theory Relat Fields. https://doi.org/10.1007/s00440-024-01318-9).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 4","pages":"1165 - 1205"},"PeriodicalIF":1.4000,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s00023-025-01561-3","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix \(X_0\), under certain assumption on \(X_0\), we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE statistics and critical statistics, which, respectively, correspond to regular and quadratic vanishing spectral points. As a continuation of our previous study on critical statistics (Liu and Zhang in Critical edge statistics for deformed GinUEs. Preprint arXiv: 2311.13227), in this paper we establish the local statistics of GinUE type at the regular spectral edge, which is characterized by a repeated erfc integral found in Liu and Zhang (Probab Theory Relat Fields. https://doi.org/10.1007/s00440-024-01318-9).
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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