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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 3, Pages 502–512
DOI: https://doi.org/10.4213/tmf9917 (Mi tmf9917) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A note on pair-dependent linear statistics with a slowly increasing variance

A. Aguirre, A. B. Soshnikov

University of California at Davis, Department of Mathematics, Davis CA, USA
Full-text PDF (432 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf9917
Abstract: We prove Gaussian fluctuations for pair-counting statistics of the form Σ1⩽i≠j⩽Nf(θi−θj) for the circular unitary ensemble of random matrices in the large-N limit under the condition that the variance increases slowly as N increases.
Keywords: random matrix, circular unitary ensemble, pair-counting statistics, central limit theorem.
Funding agency Grant number
Simons Foundation Collaboration Grant for Mathematicians 312391
This research was supported in part by the Simons Foundation (Collaboration Grant for Mathematicians No. 312391).
Received: 02.04.2020
Revised: 28.07.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 3, Pages 1682–1691
DOI: https://doi.org/10.1134/S0040577920120090
Bibliographic databases:
Document Type: Article
MSC: 60F05
Language: Russian
Citation: A. Aguirre, A. B. Soshnikov, “A note on pair-dependent linear statistics with a slowly increasing variance”, TMF, 205:3 (2020), 502–512; Theoret. and Math. Phys., 205:3 (2020), 1682–1691
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9917
  • https://doi.org/10.4213/tmf9917
  • https://www.mathnet.ru/eng/tmf/v205/i3/p502
    • This publication is cited in the following 4 articles:
    1. A. Soshnikov, “Gaussian fluctuation for smoothed local correlations in CUE”, J. Stat. Phys., 190:1 (2023), 13  crossref
    2. A. Soshnikov, C. Wu, “A note on cumulant technique in random matrix theory”, Entropy, 25:5 (2023), 725  crossref  mathscinet
    3. A. Aguirre, A. Soshnikov, “Central limit theorem for $C\beta E$ pair dependent statistics in mesoscopic regime”, Electron. Commun. Probab., 27 (2022), 1–10  crossref  mathscinet
    4. A. Aguirre, A. Soshnikov, J. Sumpter, “Pair dependent linear statistics for C beta E”, Random Matrices-Theor. Appl., 10:04 (2021), 2150035  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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