Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model

@article{Korotkikh2022HiddenDI,
  title={Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model},
  author={Sergei Korotkikh},
  journal={Probability Theory and Related Fields},
  year={2022}
}
  • S. Korotkikh
  • Published 11 May 2021
  • Mathematics
  • Probability Theory and Related Fields
We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. Because of these new parameters the previously known results about vertex models cannot be directly applied, but nevertheless the integrability remains, and we prove explicit integral expressions for q-deformed moments… 

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References

SHOWING 1-10 OF 47 REFERENCES

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

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

Observables of Stochastic Colored Vertex Models and Local Relation

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

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:

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

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

The $q$-Hahn asymmetric exclusion process

We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and

The Strict-Weak Lattice Polymer

We introduce the strict-weak polymer model, and show the KPZ universality of the free energy fluctuation of this model for a certain range of parameters. Our proof relies on the observation that the

On the integrability of zero-range chipping models with factorized steady states

The conditions of the integrability of general zero range chipping models with factorized steady states, which were proposed in Evans et al (2004 J. Phys. A: Math. Gen. 37 L275), are examined. We

On integrable directed polymer models on the square lattice

In a recent work Povolotsky (2013 J. Phys. A: Math. Theor. 46 465205) provided a three-parameter family of stochastic particle systems with zero-range interactions in one-dimension which are