A generalized dynamic asymmetric exclusion process: orthogonal dualities and degenerations

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-27 DOI:10.1088/1751-8121/ad6f7b
Wolter Groenevelt, Carel Wagenaar
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Abstract

In this paper, a generalized version of dynamic asymmetric simple exclusion process (ASEP) is introduced, and it is shown that the process has a Markov duality property with the same process on the reversed lattice. The duality functions are multivariate q-Racah polynomials, and the corresponding orthogonality measure is the reversible measure of the process. By taking limits in the generator of dynamic ASEP, its reversible measure, and the duality functions, we obtain orthogonal and triangular dualities for several other interacting particle systems. In this sense, the duality of dynamic ASEP sits on top of a hierarchy of many dualities. For the construction of the process, we rely on representation theory of the quantum algebra Uq(sl2). In the standard representation, the generator of generalized ASEP can be constructed from the coproduct of the Casimir. After a suitable change of representation, we obtain the generator of dynamic ASEP. The corresponding intertwiner is constructed from q-Krawtchouk polynomials, which arise as eigenfunctions of twisted primitive elements. This gives a duality between dynamic ASEP and generalized ASEP with q-Krawtchouk polynomials as duality functions. Using this duality, we show the (almost) self-duality of dynamic ASEP.
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广义动态非对称排斥过程:正交对偶和退化
本文介绍了动态非对称简单排除过程(ASEP)的广义版本,并证明该过程与反转网格上的同一过程具有马尔可夫对偶性。对偶函数是多元 q-Racah 多项式,相应的正交度量是过程的可逆度量。通过对动态 ASEP 的生成器、其可逆度量和对偶函数进行限值,我们得到了其他几个相互作用粒子系统的正交和三角形对偶性。从这个意义上说,动态 ASEP 的对偶性位于众多对偶性的层次之上。对于过程的构造,我们依赖于量子代数 Uq(sl2)的表示理论。在标准表示中,广义 ASEP 的发生器可以从卡西米尔的协积中构造出来。在适当改变表示之后,我们就得到了动态 ASEP 的发生器。相应的交织器由 q-Krawtchouk 多项式构造,而这些多项式是作为扭曲基元的特征函数出现的。这就给出了以 q-Krawtchouk 多项式为对偶函数的动态 ASEP 和广义 ASEP 之间的对偶性。利用这种对偶性,我们证明了动态 ASEP 的(几乎)自对偶性。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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