169 citations · 1.3k across the 50 of their papers we have counts for
51 papers
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…
Learning the symmetric group: large from small
Max Petschack, Alexandr Garbali, Jan de Gier
Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not…
Symmetric functions from the six-vertex model in half-space
Alexandr Garbali, Jan de Gier, William Mead +1
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commuta…
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…
Limit shapes for the asymmetric five vertex model
Jan de Gier, Richard Kenyon, Samuel S. Watson
We compute the free energy and surface tension function for the five-vertex model, a model of non-intersecting monotone lattice paths on the grid in which each corner gets a positi…
A curious mapping between supersymmetric quantum chains
Gyorgy Z. Feher, Alexandr Garbali, Jan de Gier +1
We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first \cite{FS07} describes semionic particles on a 1D lad…
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 $…
Integrable supersymmetric chain without particle conservation
Jan de Gier, Gyorgy Z. Feher, Bernard Nienhuis +1
We introduce a new integrable supersymmetric lattice chain which violates fermion conservation and exhibits fermion-hole symmetry. The model displays exponential degeneracy in ever…
A summation formula for Macdonald polynomials
Jan de Gier, Michael Wheeler
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the…
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,…
Exclusion in a priority queue
Jan de Gier, Caley Finn
We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low…
Traffic disruption and recovery in road networks
Lele Zhang, Timothy M. Garoni, Jan de Gier
We study the impact of disruptions on road networks, and the recovery process after the disruption is removed from the system. Such disruptions could be caused by vehicle breakdown…
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…
A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems
Lele Zhang, Timothy M. Garoni, Jan de Gier
Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different typ…
Multiple integral formula for the off-shell six vertex scalar product
Jan de Gier, Wellington Galleas, Mark Sorrell
We write a multiple integral formula for the partition function of the Z-invariant six vertex model and demonstrate how it can be specialised to compute the norm of Bethe vectors.…
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)…
Relaxation rate of the reverse biased asymmetric exclusion process
Jan de Gier, Caley Finn, Mark Sorrell
We compute the exact relaxation rate of the partially asymmetric exclusion process with open boundaries, with boundary rates opposing the preferred direction of flow in the bulk. T…