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Stochastic duality of two-component ASEP via symmetry of quantum groups of rank two

Mathematical Physics & Probability

Speaker: Jeff Kuan, Columbia University
Location: 2112 MSB
Start time: Wed, Jan 27 2016, 4:10PM

We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1. We prove that the processes are self-dual and explicitly write the duality function. The construction and proofs of duality are accomplished using symmetry of the quantum groups Uq(gl_3) and Uq(sp_4), generalizing the U_q(sl_2) symmetry of ASEP.