Stochastic six-vertex model

Borodin, Alexei; Corwin, Ivan; Gorin, Vadim

doi:10.1215/00127094-3166843

Cited by 119 publications

(217 citation statements)

References 73 publications

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“…Using (7.15) for general J and (6.5) one can write it in terms of Weil generators (6.21) similar to (6.23) It satisfies the algebra 20) where S 1,2 (λ) is given by (7.1) with I = J = 1. This L-operator was first obtained in [32] in a slightly different form.…”

Section: Stochastic R-matrixmentioning

confidence: 99%

“…Previously a closed formula for the higherspin R-matrix of the 6-vertex model was obtained in [19] based on the positive solution of the tetrahedron equation [18]. It can be interpreted as the R-matrix of the higher-spin stochastic 6-vertex model [20][21][22][23]. Under a special choice of the spectral parameter [21] this model degenerates into the q-Hahn system which corresponds to the most general "chipping model" introduced by Povolotsky [24].…”

Section: Introductionmentioning

confidence: 99%

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Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Bosnjak¹,

Mangazeev²

2016

J. Phys. A: Math. Theor.

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In this paper we construct a new factorized representation of the R-matrix related to the affine algebra U q ( sl n ) for symmetric tensor representations with arbitrary weights. Using the 3D approach we obtain explicit formulas for the matrix elements of the R-matrix and give a simple proof that a "twisted" R-matrix is stochastic. We also discuss symmetries of the R-matrix, its degenerations and compare our formulas with other results available in the literature.

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Section: Stochastic R-matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Bosnjak¹,

Mangazeev²

2016

J. Phys. A: Math. Theor.

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“…Consider (36), (37), where in each realization of (η, B L , B R ), the DP partition sum is splitted into the set of paths starting at x and ending either left or right of y = 0, The moments then split as:…”

Section: General Formula For the Moments And Generating Functionmentioning

confidence: 99%

“…Let us come back to the generating function (37). The sums over the variables m, m L , m R now become free summations leading to…”

Section: General Formula For the Moments And Generating Functionmentioning

confidence: 99%

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Crossover between various initial conditions in KPZ growth: flat to stationary

Doussal¹

2017

J. Stat. Mech.

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We conjecture the universal probability distribution at large time for the one-point height in the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality class, with initial conditions interpolating from any one of the three main classes (droplet, flat, stationary) on the left, to another on the right, allowing for drifts and also for a step near the origin. The result is obtained from a replica Bethe ansatz calculation starting from the KPZ continuum equation, together with a "decoupling assumption" in the large time limit. Some cases are checked to be equivalent to previously known results from other models in the same class, which provides a test of the method, others appear to be new. In particular we obtain the crossover distribution between flat and stationary initial conditions (crossover from Airy1 to Airystat) in a simple compact form.

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Constrained percolation, Ising model, and XOR Ising model on planar lattices

2020

Random Struct Algorithms

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We study site percolation models on planar lattices including the [m, 4, n, 4] lattice and the square tilings on the Euclidean plane (R 2 ) or the hyperbolic plane (H 2 ), satisfying certain local constraints on degree-4 faces. These models are closely related to Ising models and XOR Ising models (product of two i.i.d Ising models) on regular tilings of R 2 or H 2 . In particular, we obtain a description of the numbers of infinite "+" and "−" clusters of the ferromagnetic Ising model on a vertex-transitive triangular tiling of H 2 for different boundary conditions and coupling constants. Our results show the possibility that such an Ising configuration has infinitely many infinite "+" and "−" clusters, while its random cluster representation has no infinite open clusters. Percolation properties of corresponding XOR Ising models are also discussed.

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Stochastic six-vertex model

Cited by 119 publications

References 73 publications

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Construction ofR-matrices for symmetric tensor representations related to ${U}_{q}(\hat{{{sl}}_{n}})$

Crossover between various initial conditions in KPZ growth: flat to stationary

Constrained percolation, Ising model, and XOR Ising model on planar lattices

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