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In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices.","lang":"eng"}],"external_id":{"arxiv":["2108.13694"],"isi":["000950650200005"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"publication_status":"published","doi":"10.1214/23-ECP516","_id":"12683","article_type":"original","file_date_updated":"2023-02-27T09:43:27Z","ec_funded":1,"date_created":"2023-02-26T23:01:01Z","citation":{"apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13."},"year":"2023","acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331."},{"publication_status":"published","abstract":[{"lang":"eng","text":"We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes."}],"external_id":{"isi":["001042025400001"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"project":[{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"}],"quality_controlled":"1","volume":28,"page":"1-12","department":[{"_id":"JaMa"}],"date_published":"2023-05-05T00:00:00Z","publisher":"Institute of Mathematical Statistics","date_created":"2023-06-18T22:00:48Z","citation":{"short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12.","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023.","ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. 2023;28:1-12. doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>.","chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>.","ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12.","apa":"Dello Schiavo, L., &#38; Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>"},"year":"2023","acknowledgement":"Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208.","article_type":"original","_id":"13145","file_date_updated":"2023-06-19T09:37:40Z","doi":"10.1214/23-ECP528","author":[{"last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"},{"last_name":"Lytvynov","full_name":"Lytvynov, Eugene","first_name":"Eugene"}],"file":[{"date_created":"2023-06-19T09:37:40Z","date_updated":"2023-06-19T09:37:40Z","success":1,"checksum":"4a543fe4b3f9e747cc52167c17bfb524","file_id":"13152","file_name":"2023_ElectronCommProbability_Schiavo.pdf","file_size":271434,"relation":"main_file","access_level":"open_access","content_type":"application/pdf","creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"05","oa_version":"Published Version","publication_identifier":{"eissn":["1083-589X"]},"month":"05","status":"public","type":"journal_article","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","article_processing_charge":"No","oa":1,"date_updated":"2023-12-13T11:24:57Z","scopus_import":"1","intvolume":"        28","has_accepted_license":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Electronic Communications in Probability"}]