Stationary probabilities of the multispecies TAZRP and modified Macdonald polynomials: I

Recently, a formula for the Macdonald polynomials $P_{\lambda}(X;q,t)$ was given in terms of objects called multiline queues, which also compute probabilities of a particle model from statistical mechanics called the multispecies ASEP on a ring. It is natural to ask whether the modified Macdonald polynomials $\widetilde{H}_{\lambda}(X;q,t)$ can be obtained using a combinatorial gadget for some other statistical mechanics model. We answer this question in the affirmative. In this paper we give a new formula for $\widetilde{H}_{\lambda}(X;q,t)$ in terms of fillings of tableaux called polyqueue tableaux. In the upcoming sequel to this paper, we show that polyqueue tableaux also compute probabilities of the multispecies totally asymmetric zero range process (mTAZRP) on a ring, and that $\widetilde{H}_{\lambda}(X;1,t)$ is equal to the partition function of the mTAZRP.Comment: 44 pages, 7 figure

Modified Macdonald polynomials and the multispecies zero range process: II

In a previous part of this work, we gave a new tableau formula for the modified Macdonald polynomials $\widetilde{H}_{\lambda}(X;q,t)$, using a weight on tableaux involving the queue inversion (quinv) statistic. In this paper we establish a link between these combinatorial objects and a class of multispecies totally asymmetric zero-range processes (mTAZRP) on a ring, with site-dependent jump-rates. We construct a Markov chain on the space of tableaux of a given shape, which projects to the mTAZRP, and whose stationary distribution can be expressed in terms of quinv-weighted tableaux. We deduce that the mTAZRP has a partition function given by the modified Macdonald polynomial $\widetilde{H}_{\lambda}(X;1,t)$, and we obtain interesting symmetry properties of the mTAZRP probabilities under permutation of the jump-rates between the sites. We explore a number of interesting special cases of the mTAZRP, and give explicit formulas for particle densities and correlations of the process purely in terms of modified Macdonald polynomials.Comment: 46 pages, 7 figure

Festival quality, self-connection, and bragging

Festivals provide opportunities for experiential consumption, attracting both first-time and repeat visitors. However, current understanding of the perceptual and behavioural differences between these groups remains incomplete. This study investigates how experiential purchase quality influences experience self-connection and braggart word-of-mouth, for both first-time and repeat visitors, using a mixed-method approach. The qualitative (n=32) and quantitative (n=909) results together reveal that the combinations of experiential purchase quality dimensions stimulating experience self-connection and braggart word-of-mouth in repeat visitors differ significantly from those for first-time visitors, emphasising the need for festival managers to pay close attention to how different visitor groups perceive and prioritise experiential purchase quality dimensions. The findings thus extend current understanding of how braggart word-of-mouth emerges in an experiential consumption context

Guest editorial

Olya, H., Van Niekerk, M., Taheri, B. and Gannon, M.J. (2020), "Guest editorial", International Journal of Contemporary Hospitality Management, Vol. 32 No. 4, pp. 1385-1391. https://doi.org/10.1108/IJCHM-04-2020-02