31 citations · 165 across the 40 of their papers we have counts for
23 papers · 1 filter
Introduction to Quantum Groups and Yang-Baxter Equation For Probabilists
Jeffrey Kuan
These are a set of lecture notes for a mini-course I gave at The University of Warwick from October 30th to November 1st, 2024. Recordings of the lectures are available on Oleg Zab…
q--exchangeable Measures and Transformations in Interacting Particle Systems
Jeffrey Kuan
This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions un…
Asymptotics of dynamic ASEP using duality
Jeffrey Kuan, Zhengye Zhou
Using a recently developed method for proving asymptotics via orthogonal polynomial duality arXiv:2305.17602, we prove that the dynamic ASEP introduced in arXiv:1701.05239 has asym…
Orthogonal Dualities of Dynamic Stochastic Higher Spin Vertex Models, using the Drinfeld Twister
Jeffrey Kuan, Zhengye Zhou
We introduce a new algebraic method to construct duality functions for integrable dynamic models. This method will be implemented on dynamic stochastic higher spin vertex models, w…
Asymptotics of two-point correlations in the multi-species q-TAZRP
Jeffrey Kuan, Zhengye Zhou
A previous paper by the authors found explicit contour integral formulas for certain joint moments of the multi-species q-TAZRP (totally asymmetric zero range process), using algeb…
Orthogonal polynomial duality of a two-species asymmetric exclusion process
Danyil Blyschak, Olivia Burke, Jeffrey Kuan +3
We examine type D ASEP, a two--species interacting particle system which generalizes the usual asymmetric simple exclusion process. For certain cases of type D ASEP, the process do…
Orthogonal polynomial duality and unitary symmetries of multi--species ASEP and higher--spin vertex models via --bialgebra structure of higher rank quantum groups
Chiara Franceschini, Jeffrey Kuan, Zhengye Zhou
We propose a novel, general method to produce orthogonal polynomial dualities from the --bialgebra structure of Drinfeld--Jimbo quantum groups. The --structure allows for t…
Joint -moments and shift invariance for the multi-species -TAZRP on the infinite line
Jeffrey Kuan
This paper presents a novel method for computing certain particle locations in the multi-species -TAZRP (totally asymmetric zero range process). The method is based on a decompo…
Three-dimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices
Jeffrey Kuan, Zhengye Zhou
In arXiv:1410.7268v3, the authors consider eigenvalues of overlapping Wishart matrices and prove that its fluctuations asymptotically convergence to the Gaussian free field. In thi…
Interacting particle systems with type D symmetry and duality
Jeffrey Kuan, Mark Landry, Andrew Lin +2
We construct a two-class asymmetric interacting particle system with or symmetry, in which up to two particles may occupy a site if the two particles have d…
Determinantal Expressions in Multi-Species TASEP
Jeffrey Kuan
Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each f…
Two dualities: Markov and Schur-Weyl
Jeffrey Kuan
We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-…
A Short Note on Markov Duality in Multi-species Higher Spin Stochastic Vertex Models
Jeffrey Kuan
We show that the multi-species higher spin stochastic vertex model, also called the U_q(A_n^{(1)}) vertex model, satisfies a duality where the indicator function has the form {η^x_…
Stochastic Fusion of Interacting Particle Systems and Duality Functions
Jeffrey Kuan
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 occu…
Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups
Jeffrey Kuan
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. T…
An algebraic construction of duality functions for the stochastic U_q(A_n^{(1)}) vertex model and its degenerations
Jeffrey Kuan
A recent paper \cite{KMMO} introduced the stochastic U_q(A_n^{(1)}) vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group U_q(A_n^{(1)}) by a gauge…
Hard-edge asymptotics of the Jacobi growth process
Mark Cerenzia, Jeffrey Kuan
We introduce a two parameter () family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\{ P^{(α, β)}_k \…
A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
Jeffrey Kuan
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 ri…
An interacting particle system with geometric jump rates near a partially reflecting boundary
Jeffrey Kuan
This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to…
A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups
Jeffrey Kuan
This paper introduces a (2+1)-dimensional Gaussian field which has the Gaussian free field on the upper half-plane with zero boundary conditions as certain two-dimensional sections…
Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
Jeffrey Kuan
We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type…
Strong Szego asymptotics and zeros of the zeta function
Paul Bourgade, Jeffrey Kuan
Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions towards a Gaussian field, with covariance structure corresponding to…
Asymptotics of a discrete-time particle system near a reflecting boundary
Jeffrey Kuan
We examine a discrete-time Markovian particle system on the quarter-plane introduced by M. Defosseux. The vertical boundary acts as a reflecting wall. The particle system lies in t…