Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries

Abstract

We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial. As a corollary we obtain that the normalisation of mASEP factorises as a product over multiple copies of the two-species ASEP.

arXiv comment25 pages

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Cited by in corpus (15)

• An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
• The exact phase diagram for a class of multispecies asymmetric exclusion processes
• Combinatorial mappings of exclusion processes
• Matrix product solution to multi-species ASEP with open boundaries
• Renyi entropy of the totally asymmetric exclusion process
• A mass transport model with a simple non-factorized steady-state distribution
• Modified Macdonald polynomials and the multispecies zero range process: I
• Approximating the stationary distribution of the ASEP with open boundaries
• KPZ fluctuations in finite volume
• $T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• An exactly solvable asymmetric $K$-exclusion process
• New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes