[{"has_accepted_license":"1","department":[{"_id":"LaEr"}],"date_created":"2024-01-10T09:29:25Z","file":[{"file_name":"2023_StochasticProcAppl_Ding.pdf","file_size":1870349,"date_created":"2024-01-16T08:47:31Z","checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","date_updated":"2024-01-16T08:47:31Z","access_level":"open_access","success":1,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"14806"}],"month":"09","date_published":"2023-09-01T00:00:00Z","article_type":"original","publisher":"Elsevier","language":[{"iso":"eng"}],"publication":"Stochastic Processes and their Applications","page":"25-60","file_date_updated":"2024-01-16T08:47:31Z","day":"01","type":"journal_article","intvolume":"       163","status":"public","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"ddc":["510"],"year":"2023","doi":"10.1016/j.spa.2023.05.009","ec_funded":1,"external_id":{"arxiv":["2302.13502"],"isi":["001113615900001"]},"title":"Spiked multiplicative random matrices and principal components","arxiv":1,"article_processing_charge":"Yes (in subscription journal)","oa":1,"date_updated":"2024-01-16T08:49:51Z","volume":163,"publication_identifier":{"issn":["0304-4149"],"eissn":["1879-209X"]},"_id":"14780","oa_version":"Published Version","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","citation":{"ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol. 163, Elsevier, 2023, pp. 25–60, doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>.","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>.","apa":"Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier, pp. 25–60, 2023."},"publication_status":"published","abstract":[{"lang":"eng","text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix."}],"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"author":[{"full_name":"Ding, Xiucai","last_name":"Ding","first_name":"Xiucai"},{"last_name":"Ji","full_name":"Ji, Hong Chang","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}]},{"article_type":"original","date_published":"2021-08-27T00:00:00Z","month":"08","language":[{"iso":"eng"}],"publisher":"Elsevier","scopus_import":"1","department":[{"_id":"JaMa"}],"has_accepted_license":"1","date_created":"2021-09-19T22:01:25Z","file":[{"file_size":2115791,"file_name":"2021_StochasticProcessesAppl_Floreani.pdf","checksum":"56768c553d7218ee5714902ffec90ec4","date_created":"2022-05-13T07:55:50Z","access_level":"open_access","date_updated":"2022-05-13T07:55:50Z","success":1,"relation":"main_file","content_type":"application/pdf","file_id":"11370","creator":"dernst"}],"type":"journal_article","day":"27","status":"public","intvolume":"       142","page":"124-158","file_date_updated":"2022-05-13T07:55:50Z","publication":"Stochastic Processes and their Applications","ec_funded":1,"year":"2021","doi":"10.1016/j.spa.2021.08.006","external_id":{"arxiv":["1911.12564"],"isi":["000697748500005"]},"title":"Hydrodynamics for the partial exclusion process in random environment","isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["519"],"publication_status":"published","citation":{"chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>.","apa":"Floreani, S., Redig, F., &#38; Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>","ieee":"S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” <i>Stochastic Processes and their Applications</i>, vol. 142. Elsevier, pp. 124–158, 2021.","ista":"Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158.","short":"S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158.","mla":"Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>, vol. 142, Elsevier, 2021, pp. 124–58, doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>.","ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and their Applications</i>. 2021;142:124-158. doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>"},"author":[{"last_name":"Floreani","full_name":"Floreani, Simone","first_name":"Simone"},{"last_name":"Redig","full_name":"Redig, Frank","first_name":"Frank"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","last_name":"Sau","full_name":"Sau, Federico"}],"keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"abstract":[{"text":"In this paper, we introduce a random environment for the exclusion process in  obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020).","lang":"eng"}],"volume":142,"oa":1,"date_updated":"2023-08-14T06:52:43Z","article_processing_charge":"Yes","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and  Cristian  Giardina,  Frank  den  Hollander  and  Shubhamoy  Nandan  for  inspiring  discussions.  S.F.  acknowledges  Simona  Villa  for  her  help  in  creating  the  picture.  Furthermore, the  authors  thank  two  anonymous  referees  for  the  careful  reading  of  the  manuscript.  S.F. acknowledges  financial  support  from  NWO,  The  Netherlands  via  the  grant  TOP1.17.019. F.S.  acknowledges  financial  support  from  NWO  via  the  TOP1  grant  613.001.552  as  well  as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","oa_version":"Published Version","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"quality_controlled":"1","_id":"10024","publication_identifier":{"issn":["0304-4149"]}}]