Observables of Stochastic Colored Vertex Models and Local Relation

@article{Bufetov2021ObservablesOS,
  title={Observables of Stochastic Colored Vertex Models and Local Relation},
  author={Alexey Bufetov and Sergei Korotkikh},
  journal={Communications in Mathematical Physics},
  year={2021}
}
We study the stochastic colored six vertex (SC6V) model and its fusion. Our main result is an integral expression for natural observables of this model -- joint q-moments of height functions. This generalises a recent result of Borodin-Wheeler. The key technical ingredient is a new relation of height functions of SC6V model in neighboring points. This relation is of independent interest; we refer to it as a local relation. As applications, we give a new proof of certain symmetries of height… 

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References

SHOWING 1-10 OF 31 REFERENCES

Symmetries of stochastic colored vertex models

Author(s): Galashin, Pavel | Abstract: We discover a new property of the stochastic colored six-vertex model called flip invariance. We use it to show that for a given collection of observables of

Higher spin six vertex model and symmetric rational functions

We consider a fully inhomogeneous stochastic higher spin six vertex model in a quadrant. For this model we derive concise integral representations for multi-point q-moments of the height function and

Stochastic Higher Spin Vertex Models on the Line

We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain

Coloured stochastic vertex models and their spectral theory

This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following:

Shift‐invariance for vertex models and polymers

We establish a symmetry in a variety of integrable stochastic systems: certain multi‐point distributions of natural observables are unchanged under a shift of a subset of observation points. The

Observables of coloured stochastic vertex models and their polymer limits

In the context of the coloured stochastic vertex model in a quadrant, we identify a family of observables whose averages are given by explicit contour integrals. The observables are certain linear

Stochastic six-vertex model

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit

Hall–Littlewood RSK field

We introduce a randomized Hall–Littlewood RSK algorithm and study its combinatorial and probabilistic properties. On the probabilistic side, a new model—the Hall–Littlewood RSK field—is introduced.

Color-position symmetry in interacting particle systems

We prove a color-position symmetry for a class of ASEP-like interacting particle systems with discrete time on the one-dimensional lattice. The full space-time inhomogeneity of our systems allows to