Orthogonal Stochastic Duality Functions from Lie Algebra Representations
Orthogonal Stochastic Duality Functions from Lie Algebra Representations
复制标题
李代数表示的正交随机对偶函数
DOI：
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发表时间：
2017
影响因子：
1.6
通讯作者：
W. Groenevelt
中科院分区：
文献类型：
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作者：
W. Groenevelt
利用李代数的表示理论，得到了特定马尔可夫过程的随机对偶函数。对偶函数来自于一个一元交织器的内核，它是在两个表示之间（∗documentclass[12pt]{minimal} uspackage {amsmath} uspackage {wasysym} uspackage {amsfonts} uspackage {amssymb} uspackage {amssyb} uspackage {mathrsfs} uspackage {upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$*$$end{document}）提供了对偶函数的（广义的）正交关系。特别地，我们考虑海森堡代数和su(1,1)documentclass[12pt]{minimal} uspackage {amsmath} uspackage {wasysym} uspackage {amsfonts} uspackage {amssymb} uspackage {amssyb} uspackage {mathrsfs} uspackage {upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathfrak {su}(1,1)$$end{document}的表示。这两种情况导致正交（自）对偶函数的超几何函数的特定相互作用的粒子过程和相互作用的扩散过程。
We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between ∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$*$$end{document}-representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and su(1,1)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathfrak {su}(1,1)$$end{document}. Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes.
影响因子：
1.6
作者：
Jansen, Sabine;Kurt, Noemi
通讯作者：
Kurt, Noemi