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Stable spin Hall-Littlewood symmetric functions, combinatorial identities, and half-space Yang-Baxter random field
- Mathematics
- 2021
Abstract. Stable spin Hall-Littlewood symmetric polynomials labeled by partitions were recently introduced by Borodin and Wheeler in the context of higher spin six vertex models, which are…
Refined Cauchy identity for spin Hall-Littlewood symmetric rational functions
- MathematicsJ. Comb. Theory, Ser. A
- 2021
Spin q-Whittaker polynomials and deformed quantum Toda.
- Mathematics
- 2020
Spin $q$-Whittaker symmetric polynomials labeled by partitions $\lambda$ were recently introduced by Borodin and Wheeler (arXiv:1701.06292) in the context of integrable $\mathfrak{sl}_2$ vertex…
Parameter Permutation Symmetry in Particle Systems and Random Polymers
- Mathematics
- 2021
Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its various deformations, with a notable exception of ASEP)…
Mapping TASEP back in time
- MathematicsProbability Theory and Related Fields
- 2021
We obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the…
Inhomogeneous spin $q$-Whittaker polynomials
- Mathematics
- 2021
We introduce and study an inhomogeneous generalization of the spin q-Whittaker polynomials from [BW17]. These are symmetric polynomials, and we prove a branching rule, skew dual and non-dual Cauchy…
Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays
- MathematicsAnnales Henri Poincare
- 2020
It is shown that for a certain class of initial conditions the point process associated with the dynamics has determinantal correlation functions, and the correlation kernel for one of the most classical initial conditions, the densely packed is calculated.
Identity between restricted Cauchy sums for the $q$-Whittaker and skew Schur polynomials
- Mathematics
- 2021
The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the q-Whittaker and the skew Schur polynomials produce the same factorized…
A Lattice Model for Super LLT Polynomials
- Mathematics
- 2021
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock…
PushTASEP in inhomogeneous space
- Mathematics, Physics
- 2019
We consider the PushTASEP (pushing totally asymmetric simple exclusion process, also sometimes called long-range TASEP) with the step initial configuration evolving in an inhomogeneous space. That…
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