Censored processes, that is processes in which certain transitions have been disallowed, have been a key tool in understanding monotone spin systems and some other Markov chains.
In this talk we introduce a censored version of the stochastic six-vertex model and give as the main result of this work a censoring inequality for this model.In the proof of this result we used certain polynomials, which turn out to be the parabolic Kazhdan-Lusztig R-polynomials.
We were able to explain their appearance using a recently established connection of the colored stochastic six-vertex model and Iwatori-Hecke algebras.
I will end this talk by giving a novel symmetry of the model which uses the Kazhdan-Lusztig R-polynomials as an intertwining kernel.
Based on joint work with Hindy Drillick
Paper on arxiv at arxiv.org/abs/2606.12670