{"title":"具有3个相互作用粒子的共轭Kac过程的谱隙下界","authors":"L. Ferreira","doi":"10.3934/krm.2021045","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we proceed as suggested in the final section of [<xref ref-type=\"bibr\" rid=\"b2\">2</xref>] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around <inline-formula><tex-math id=\"M1\">\\begin{document}$ 0.02 $\\end{document}</tex-math></inline-formula>, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"21 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles\",\"authors\":\"L. Ferreira\",\"doi\":\"10.3934/krm.2021045\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p style='text-indent:20px;'>In this paper, we proceed as suggested in the final section of [<xref ref-type=\\\"bibr\\\" rid=\\\"b2\\\">2</xref>] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around <inline-formula><tex-math id=\\\"M1\\\">\\\\begin{document}$ 0.02 $\\\\end{document}</tex-math></inline-formula>, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.</p>\",\"PeriodicalId\":49942,\"journal\":{\"name\":\"Kinetic and Related Models\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kinetic and Related Models\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/krm.2021045\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kinetic and Related Models","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/krm.2021045","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
In this paper, we proceed as suggested in the final section of [2] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around \begin{document}$ 0.02 $\end{document}, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.
A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles
In this paper, we proceed as suggested in the final section of [2] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around \begin{document}$ 0.02 $\end{document}, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.
期刊介绍:
KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.