[{"doi":"10.1007/s44007-025-00180-y","abstract":[{"lang":"eng","text":"In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the Lebesgue and the Gaussian measures, and discuss their differences in terms of moments and stability. We give new and direct proofs, as well as examples and discuss the stability of a logarithmic uncertainty principle. Although we do not cover all aspects of the topic, we hope to contribute to establishing the state of the art."}],"arxiv":1,"OA_type":"hybrid","article_number":"5","article_processing_charge":"Yes (via OA deal)","citation":{"ieee":"G. Brigati, J. Dolbeault, and N. Simonov, “Logarithmic Sobolev Inequalities: A review on stability and instability results,” <i>La Matematica</i>, vol. 5. Springer Nature, 2026.","apa":"Brigati, G., Dolbeault, J., &#38; Simonov, N. (2026). Logarithmic Sobolev Inequalities: A review on stability and instability results. <i>La Matematica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s44007-025-00180-y\">https://doi.org/10.1007/s44007-025-00180-y</a>","ista":"Brigati G, Dolbeault J, Simonov N. 2026. Logarithmic Sobolev Inequalities: A review on stability and instability results. La Matematica. 5, 5.","short":"G. Brigati, J. Dolbeault, N. Simonov, La Matematica 5 (2026).","ama":"Brigati G, Dolbeault J, Simonov N. Logarithmic Sobolev Inequalities: A review on stability and instability results. <i>La Matematica</i>. 2026;5. doi:<a href=\"https://doi.org/10.1007/s44007-025-00180-y\">10.1007/s44007-025-00180-y</a>","mla":"Brigati, Giovanni, et al. “Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results.” <i>La Matematica</i>, vol. 5, 5, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s44007-025-00180-y\">10.1007/s44007-025-00180-y</a>.","chicago":"Brigati, Giovanni, Jean Dolbeault, and Nikita Simonov. “Logarithmic Sobolev Inequalities: A Review on Stability and Instability Results.” <i>La Matematica</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s44007-025-00180-y\">https://doi.org/10.1007/s44007-025-00180-y</a>."},"_id":"21018","scopus_import":"1","file":[{"file_id":"21025","date_created":"2026-01-21T07:45:03Z","creator":"dernst","file_size":4992025,"date_updated":"2026-01-21T07:45:03Z","checksum":"0702d8397f216555b1d5286e5d77f09c","access_level":"open_access","relation":"main_file","success":1,"file_name":"2026_LaMatematica_Brigati.pdf","content_type":"application/pdf"}],"PlanS_conform":"1","type":"journal_article","year":"2026","title":"Logarithmic Sobolev Inequalities: A review on stability and instability results","file_date_updated":"2026-01-21T07:45:03Z","article_type":"original","external_id":{"arxiv":["2504.08658"]},"corr_author":"1","oa_version":"Published Version","ddc":["510"],"quality_controlled":"1","day":"08","department":[{"_id":"JaMa"}],"publication_status":"published","month":"01","date_updated":"2026-01-21T07:48:28Z","author":[{"last_name":"Brigati","first_name":"Giovanni","full_name":"Brigati, Giovanni","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1"},{"full_name":"Dolbeault, Jean","last_name":"Dolbeault","first_name":"Jean"},{"full_name":"Simonov, Nikita","first_name":"Nikita","last_name":"Simonov"}],"acknowledgement":"This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the French National Research Agency. G.B. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. The authors thank a referee for a careful reading and suggestions which result in a significant improvement of the manuscript. Open access funding provided by Institute of Science and Technology (IST Austria). The work of GB has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. This work has been supported by the Project Conviviality (ANR-23-CE40–0003) of the French National Research Agency.","volume":5,"date_created":"2026-01-20T10:14:55Z","has_accepted_license":"1","publisher":"Springer Nature","ec_funded":1,"publication_identifier":{"issn":["2730-9657"]},"OA_place":"publisher","oa":1,"publication":"La Matematica","project":[{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"intvolume":"         5","status":"public","date_published":"2026-01-08T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]