Groenevelt Wolter
Technische Universiteit Delft, DIAM, PO Box 5031, 2600 GA Delft, The Netherlands.
J Stat Phys. 2019;174(1):97-119. doi: 10.1007/s10955-018-2178-7. Epub 2018 Oct 19.
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 -representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and . Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes.
我们利用李代数的表示理论为特定的马尔可夫过程获得随机对偶函数。对偶函数来自于 - 表示之间酉交织算子的核，它为对偶函数提供了（广义）正交关系。特别地，我们考虑海森堡代数和 的表示。这两种情况都导致了针对特定相互作用粒子过程和相互作用扩散过程的用超几何函数表示的正交（自）对偶函数。
