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Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data 具有不确定性数据的非线性抛物型方程的拟可逆性方法分析
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-9501497
N. Tuan, Erkan Nane, D. D. Trong
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引用次数: 1
Mixing and hitting times for Gibbs samplers and other non-Feller processes 吉布斯采样器和其他非费勒过程的混合和击打时间
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-9421096
R. Anderson, Haosui Duanmu, Aaron Smith
{"title":"Mixing and hitting times for Gibbs samplers and other non-Feller processes","authors":"R. Anderson, Haosui Duanmu, Aaron Smith","doi":"10.1215/00192082-9421096","DOIUrl":"https://doi.org/10.1215/00192082-9421096","url":null,"abstract":"The hitting and mixing times are two often-studied quantities associated with Markov chains. Yuval Peres, Perla Sousi and Roberto Oliveira showed that the mixing times and “worst-case” hitting times of reversible Markov chains on finite state spaces are “equivalent”—that is, equal up to some universal multiplicative constant. We have extended this strong connection between mixing and hitting times to Markov chains satisfying the strong Feller property in an earlier work. In the present paper, we further extend the results to include Metropolis–Hastings chains, the popular Gibbs sampler (from statistics), and Glauber dynamics (from statistical physics), which make “one-dimensional” updates and thus do not satisfy the strong Feller property. We also apply this result to obtain decomposition bounds for such Markov chains. Our main tools come from nonstandard analysis.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
An optimization problem arising in CR geometry CR几何中的一个优化问题
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-8947202
J. D'Angelo
{"title":"An optimization problem arising in CR geometry","authors":"J. D'Angelo","doi":"10.1215/00192082-8947202","DOIUrl":"https://doi.org/10.1215/00192082-8947202","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"-1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Vlasov–Poisson–Fokker–Planck equation in E2,1s space E2,1s空间中的Vlasov-Poisson-Fokker-Planck方程
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-9402086
Jingchun Chen, Cong He
{"title":"Vlasov–Poisson–Fokker–Planck equation in E2,1s space","authors":"Jingchun Chen, Cong He","doi":"10.1215/00192082-9402086","DOIUrl":"https://doi.org/10.1215/00192082-9402086","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian 非对称拉普拉斯算子ε-范围下N权Ricci曲率下界上的刚性现象
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-9619586
K. Kuwae, Y. Sakurai
{"title":"Rigidity phenomena on lower N-weighted Ricci curvature bounds with ε-range for nonsymmetric Laplacian","authors":"K. Kuwae, Y. Sakurai","doi":"10.1215/00192082-9619586","DOIUrl":"https://doi.org/10.1215/00192082-9619586","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41541131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Complete spacelike hypersurfaces with constant scalar curvature: Descriptions and gaps 具有恒定标量曲率的完全类空间超曲面:描述和间隙
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-9619615
A. Colares, Eudes L. de Lima, H. D. de Lima
{"title":"Complete spacelike hypersurfaces with constant scalar curvature: Descriptions and gaps","authors":"A. Colares, Eudes L. de Lima, H. D. de Lima","doi":"10.1215/00192082-9619615","DOIUrl":"https://doi.org/10.1215/00192082-9619615","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45412520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Weighted inequalities for q-functions q函数的加权不等式
IF 0.6
Illinois Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1215/00192082-8946105
T. Gałązka, A. Osȩkowski
{"title":"Weighted inequalities for q-functions","authors":"T. Gałązka, A. Osȩkowski","doi":"10.1215/00192082-8946105","DOIUrl":"https://doi.org/10.1215/00192082-8946105","url":null,"abstract":"Let f be a martingale on an arbitrary atomic probability space equipped with a tree-like structure and let S(f, q) denote the associated q-function. The paper is devoted to weighted Lp-estimates c−1 p,q,w‖S(f, q)‖Lp(w) ≤ ‖f‖Lp(w) ≤ Cp,q,w‖S(f, q)‖Lp(w), 1 ≤ p <∞, for Muckenhoupt weights. Using the combination of the theory of sparse operators, extrapolation and Bellman function method, we identify the optimal dependence of the constants cp,q,w and Cp,q,w on the Ap characteristics of the weights involved.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"-1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Banach space representations of Drinfeld–Jimbo algebras and their complex-analytic forms Drinfeld-Jimbo代数的Banach空间表示及其复解析形式
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-12-23 DOI: 10.1215/00192082-10592466
O. Aristov
{"title":"Banach space representations of Drinfeld–Jimbo algebras and their complex-analytic forms","authors":"O. Aristov","doi":"10.1215/00192082-10592466","DOIUrl":"https://doi.org/10.1215/00192082-10592466","url":null,"abstract":"We prove that every non-degenerate Banach space representation of the Drinfeld-Jimbo algebra $U_q(mathfrak{g})$ of a semisimple complex Lie algebra $mathfrak{g}$ is finite dimensional when $|q|ne 1$. As a corollary, we find an explicit form of the Arens-Michael envelope of $U_q(mathfrak{g})$, which is similar to that of $U(mathfrak{g})$ obtained by Joseph Taylor in 70s. In the case when $mathfrak{g}=mathfrak{s}mathfrak{l}_2$, we also consider the representation theory of the corresponding analytic form $widetilde U(mathfrak{s}mathfrak{l}_2)_hbar$ (with $e^hbar=q$) and show that it is simpler than for $U_q(mathfrak{s}mathfrak{l}_2)$. For example, all irreducible continuous representations of $widetilde U(mathfrak{s}mathfrak{l}_2)_hbar$ are finite dimensional for every admissible value of the complex parameter $hbar$, while $U_q(mathfrak{s}mathfrak{l}_2)$ has a topologically irreducible infinite-dimensional representation when $|q|= 1$ and $q$ is not a root of unity.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43886872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extremal parameters and their duals for boundary maps associated to Fuchsian groups 与Fuchsian群相关的边界图的极值参数及其对偶
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-12-01 DOI: 10.1215/00192082-8827631
Adam Abrams
{"title":"Extremal parameters and their duals for boundary maps associated to Fuchsian groups","authors":"Adam Abrams","doi":"10.1215/00192082-8827631","DOIUrl":"https://doi.org/10.1215/00192082-8827631","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42112366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Zeros of Gaussian power series with dependent random variables 具有相关随机变量的高斯幂级数的零
IF 0.6
Illinois Journal of Mathematics Pub Date : 2020-12-01 DOI: 10.1215/00192082-8720490
Safari Mukeru, M. Mulaudzi, J. Nzabanita, Marc Mukendi Mpanda
{"title":"Zeros of Gaussian power series with dependent random variables","authors":"Safari Mukeru, M. Mulaudzi, J. Nzabanita, Marc Mukendi Mpanda","doi":"10.1215/00192082-8720490","DOIUrl":"https://doi.org/10.1215/00192082-8720490","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"64 1","pages":"569-582"},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49208694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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