From multiline queues to Macdonald polynomials via the exclusion process

Recently James Martin introduced multiline queues, and used them to give a formula for the stationary distribution of the multispecies simple exclusion exclusion process (ASEP) on a circle. The ASEP is a of particles hopping on a one-dimensional lattice, which was introduced 1970, and has been extensively studied in statistical mechanics,, and combinatorics. In this article we give an independent proof of's result, and we show that by introducing additional statistics on queues, we can use them to give a new combinatorial formula for both symmetric Macdonald polynomials Plambda(x; q, t), and the nonsymmetric polynomials Elambda(x; q, t), where lambda is a partition. This is rather different from others that have appeared in the literature, as the formulas due to Haglund, Haiman, and Loehr, the formula due to Ram Yip, and the one due to Lenart. Our proof uses results of Cantini, de Gier, Wheeler, who recently linked the multispecies ASEP on a circle to Macdonald.