3 Citations
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 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…
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…
References
SHOWING 1-10 OF 23 REFERENCES
Color-position symmetry in interacting particle systems
- MathematicsThe Annals of Probability
- 2019
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…
Interacting Particle Systems
- Mathematics
- 1985
The Construction, and Other General Results.- Some Basic Tools.- Spin Systems.- Stochastic Ising Models.- The Voter Model.- The Contact Process.- Nearest-Particle Systems.- The Exclusion Process.-…
Stochastic Fusion of Interacting Particle Systems and Duality Functions
- Mathematics
- 2019
We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site.…
The TASEP speed process.
- Mathematics
- 2011
In the multi-type totally asymmetric simple exclusion process (TASEP), each site ofZ is occupied by a labeled particle, and two neighboring particles are int erchanged at rate one if their labels are…
Hydrodynamic equations for attractive particle systems on ℤ
- Mathematics
- 1987
Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as…
Probability Distributions of Multi-species q-TAZRP and ASEP as Double Cosets of Parabolic Subgroups
- MathematicsAnnales Henri Poincaré
- 2019
We write explicit contour integral formulas for probability distributions of the multi-species q-TAZRP and the multi-species ASEP starting with q-exchangeable initial conditions. The formulas are…
The oriented swap process.
- Mathematics
- 2009
Particles labelled 1, ..., n are initially arranged in increasing order. Subsequently, each pair of neighboring particles that is currently in increasing order swaps according to a Poisson process of…
A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
- Mathematics
- 2018
This paper introduces a multi-species version of a process called ASEP(q,j). In this process, up to 2j particles are allowed to occupy a lattice site, the particles drift to the right with asymmetry…
A generalized asymmetric exclusion process with $$U_q(\mathfrak {sl}_2)$$Uq(sl2) stochastic duality
- Mathematics
- 2015
We study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $$q\in (0,1)$$q∈(0,1) and where at most $$2j\in…
Finite groups of Lie type: Conjugacy classes and complex characters
- Mathematics
- 1985
BN-Pairs and Coxeter Groups. Maximal Tori and Semisimple Classes. Geometric Conjugacy and Duality. Unipotent Classes. The Steinberg Character. The Generalized Characters of Deligne-Lusztig. Further…