Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
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通过二阶量子群的对称性，具有两种粒子类型的 ASEP 的随机对偶性
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发表时间：
2015
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通讯作者：
Jeffrey Kuan
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文献类型：
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作者：
Jeffrey Kuan
本文研究了两类粒子的非对称简单不相容过程（ASEP）的两种推广，分别称为A2型ASEP和C2型ASEP。第一类粒子迫使第二类粒子交换位置。C2情况下，2类粒子只会影响1类粒子的跳跃速率，A2情况下，2类粒子对1类粒子完全没有影响。我们证明了过程是自对偶的，并显式地写出了对偶函数，这是对ASEP的自对偶函数的推广。对偶性的构造和证明是利用量子群的对称性q (gl 3) ？>和q (sp4) ？A2和C2 ASEP分别为>。
We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles, which will be called type A2 ASEP and type C2 ASEP. Particles of type 1 force particles of type 2 to switch places. In the C2 case, particles of type 2 can only influence the jump rates of particles of type 1, and in the A2 case particles of type 2 do not influence particles of type 1 at all. We prove that the processes are self-dual and explicitly write the duality function, which is a generalization of the self-duality function for ASEP. The construction and proofs of duality are accomplished using symmetry of the quantum groups q ( gl 3 ) ?> and q ( sp 4 ) ?> for the A2 and C2 ASEP respectively.