Shift‐invariance for vertex models and polymers
@article{Borodin2022ShiftinvarianceFV, title={Shift‐invariance for vertex models and polymers}, author={Alexei Borodin and Vadim Gorin and Michael Wheeler}, journal={Proceedings of the London Mathematical Society}, year={2022}, volume={124} }
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 property holds for stochastic vertex models, (1+1)d directed polymers in random media, last passage percolation, the Kardar–Parisi–Zhang equation, and the Airy sheet. In each instance it leads to computations of previously inaccessible joint distributions. The proofs rely on a combination of the Yang…
Figures from this paper
15 Citations
Symmetries of stochastic colored vertex models
- MathematicsThe Annals of Probability
- 2021
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…
Shift invariance of half space integrable models
- Mathematics
- 2022
. We formulate and establish symmetries of certain integrable half space models, analogous to recent results on symmetries for models in a full space. Our starting point is the colored stochastic six…
Observables of coloured stochastic vertex models and their polymer limits
- Mathematics
- 2020
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…
Hidden invariance of last passage percolation and directed polymers
- MathematicsThe Annals of Probability
- 2022
Last passage percolation and directed polymer models on $\mathbb{Z}^2$ are invariant under translation and certain reflections. When these models have an integrable structure coming from either the…
Observables of Stochastic Colored Vertex Models and Local Relation
- MathematicsCommunications in Mathematical Physics
- 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…
Hidden diagonal integrability of q-Hahn vertex model and Beta polymer model
- MathematicsProbability Theory and Related Fields
- 2022
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…
The geometric Burge correspondence and the partition function of polymer replicas
- MathematicsSelecta Mathematica
- 2021
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric…
Invariance of polymer partition functions under the geometric RSK correspondence
- Mathematics
- 2020
We prove that the values of discrete directed polymer partition functions involving multiple non-intersecting paths remain invariant under replacing the background weights by their images under the…
Absorbing time asymptotics in the oriented swap process
- MathematicsThe Annals of Applied Probability
- 2022
The oriented swap process is a natural directed random walk on the symmetric group that can be interpreted as a multi-species version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a…
Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics, and spiked random matrices: Pinning and localization.
- PhysicsPhysical review. E
- 2021
It is found that for a single line and a single strong defect this transition in the presence of point disorder coincides with the Baik-Ben Arous-Péché (BBP) transition for the appearance of outliers in the spectrum of a perturbed random matrix in the Gaussian unitary ensemble.
References
SHOWING 1-10 OF 71 REFERENCES
Stochastic Higher Spin Vertex Models on the Line
- Mathematics
- 2015
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…
Renormalization Fixed Point of the KPZ Universality Class
- Mathematics
- 2011
The one dimensional Kardar–Parisi–Zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents. These exponents lead to a…
The Continuum Directed Random Polymer
- Mathematics
- 2014
Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white…
The Kardar-Parisi-Zhang equation and universality class
- Mathematics
- 2011
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or…
Observables of Stochastic Colored Vertex Models and Local Relation
- MathematicsCommunications in Mathematical Physics
- 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…
Stochastic PDE Limit of the Six Vertex Model
- MathematicsCommunications in Mathematical Physics
- 2020
We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $$\Delta \rightarrow 1^+$$ Δ → 1 + so as to zoom into the ferroelectric/disordered phase…
Higher spin six vertex model and symmetric rational functions
- Mathematics
- 2016
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…
Coloured stochastic vertex models and their spectral theory
- Mathematics
- 2018
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: …
The directed landscape
- Mathematics
- 2018
The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage…