169 citations · 1.3k across the 50 of their papers we have counts for
20 papers · 1 filter
The asymmetric five vertex model on a rectangle
Jan de Gier, Richard Kenyon, Michael Wheeler +1
We derive a determinantal expression for the inhomogeneous asymmetric five vertex model in a rectangular geometry with arbitrary boundary conditions at the bottom and top. Standard…
Intertwining Markov Processes via Matrix Product Operators
Rouven Frassek, Jan de Gier, Jimin Li +1
Duality transformations reveal unexpected equivalences between seemingly distinct models. We introduce an out-of-equilibrium generalisation of matrix product operators to implement…
Transition probability and total crossing events in the multi-species asymmetric exclusion process
Jan de Gier, William Mead, Michael Wheeler
We present explicit formulas for total crossing events in the multi-species asymmetric exclusion process (-ASEP) with underlying symmetry. I…
Limiting current distribution for a two species asymmetric exclusion process
Zeying Chen, Jan de Gier, Iori Hiki +2
We study current fluctuations of a two-species asymmetric exclusion process, known as the Arndt-Heinzel-Rittenberg model. For a step-Bernoulli initial condition with finite number…
The -matrix of the quantum toroidal algebra in the Fock module
Alexandr Garbali, Jan de Gier
We propose a method to compute the -matrix on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We apply this method to the quantum toroidal algeb…
Integrable stochastic dualities and the deformed Knizhnik-Zamolodchikov equation
Zeying Chen, Jan de Gier, Michael Wheeler
We present a new method for obtaining duality functions in multi-species asymmetric exclusion processes (mASEP), from solutions of the deformed Knizhnik-Zamolodchikov equations. Ou…
Finite-size corrections for universal boundary entropy in bond percolation
Jan de Gier, Jesper Lykke Jacobsen, Anita Ponsaing
We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a c…
Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
Luigi Cantini, Alexandr Garbali, Jan de Gier +1
We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial. As a corol…
A new generalisation of Macdonald polynomials
Alexandr Garbali, Jan de Gier, Michael Wheeler
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters and polynomial in a further two parameters $…
Matrix product formula for Macdonald polynomials
Luigi Cantini, Jan de Gier, Michael Wheeler
We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik--Zamolodchikov equations,…
Discrete holomorphicity and integrability in loop models with open boundaries
Jan de Gier, Alexander Lee, Jorgen Rasmussen
We consider boundary conditions compatible with discrete holomorphicity for the dilute O(n) and C_2^(1) loop models. In each model, for a general set of boundary plaquettes, multip…
Off-critical parafermions and the winding angle distribution of the O() model
Andrew Elvey Price, Jan de Gier, Anthony J. Guttmann +1
Using an off-critical deformation of the identity of Duminil-Copin and Smirnov, we prove a relationship between half-plane surface critical exponents and as well as…
The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is
Nicholas R. Beaton, Mireille Bousquet-Mélou, Jan de Gier +2
In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb)…
Separation of variables for symplectic characters
Jan de Gier, Anita Ponsaing
We perform separation of variables for the symplectic Weyl character using Sklyanin's scheme. Viewing the characters as eigenfunctions of a quantum integrable system, we explicitly…
Exact spin quantum Hall current between boundaries of a lattice strip
Jan de Gier, Bernard Nienhuis, Anita Ponsaing
Employing an inhomogeneous solvable lattice model, we derive an exact expression for a boundary-to-boundary edge current on a lattice of finite width. This current is an example of…
Factorised solutions of Temperley-Lieb KZ equations on a segment
Jan de Gier, Pavel Pyatov
We study the q-deformed Knizhnik-Zamolodchikov equation in path representations of the Temperley-Lieb algebras. We consider two types of open boundary conditions, and in both cases…
Temperley-Lieb Stochastic Processes
Paul A. Pearce, Vladimir Rittenberg, Jan de Gier +1
We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjectur…
The Rotor Model and Combinatorics
M. T. Batchelor, J. de Gier, B. Nienhuis
We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign m…
The XXZ spin chain at : Bethe roots, symmetric functions and determinants
Jan de Gier, Murray Batchelor, Bernard Nienhuis +1
A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at and various symmetry classes of alternatin…
Six - Vertex Model with Domain wall boundary conditions. Variable inhomogeneities
J. de Gier, V. Korepin
We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have man…