Tail probabilities of the stochastic six vertex model.

Promit Ghosal
Brandeis University

We explore the tail probabilities of stochastic six-vertex models using the q-moments formula of their height function. Borodin and Olshanski (2016) established an identity linking the q-moments of the stochastic six-vertex model to a multiplicative functional of the Meixner orthogonal polynomial ensemble. Our investigation reveals that the tail probabilities of these models undergo multiple transitions, governed by various integrable differential equations such as Painlevé XXXIV and Bessel differential equations in distinct phases. Employing Riemann-Hilbert techniques, we derive asymptotic behaviors, with the potential to extend this analysis to understand the asymptotics of multiplicative functionals of other discrete orthogonal polynomial ensembles. This presentation will draw from an upcoming collaborative work with Guilherme Silva.

Back to Workshop IV: Vertex Models: Algebraic and Probabilistic Aspects of Universality