31 citations · 165 across the 40 of their papers we have counts for
41 papers
Correlated and uncorrelated long--time asymptotics of type D ASEP
Jeffrey Kuan
The type D ASEP is an asymmetric two--species interacting particle system on , in which two separately conserved species hop, bind into a composite ``bound pair'', and split. T…
Using Large Language Models as a Co-Author in Undergraduate Quantum Group Research
Jeffrey Kuan
This article describes the use of Claude CLI and its Opus 4.6 model, as a tool for writing an entirely AI-generated mathematics research paper. The resulting paper is comparable in…
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…
Fluid-poroviscoelastic structure interaction problem with nonlinear geometric coupling
Jeffrey Kuan, Sunčica Čanić, Boris Muha
We investigate weak solutions to a fluid-structure interaction (FSI) problem between the flow of an incompressible, viscous fluid modeled by the Navier-Stokes equations, and a poro…
An explicit central element of and its corresponding quantum Hamiltonian
Jeffrey Kuan
A previous paper of the author developed a general method for producing explicit central elements of quantized Lie algebras using Lusztig's inner product. This method had previousl…
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…
Well-posedness of solutions to stochastic fluid-structure interaction
Jeffrey Kuan, Sunčica Čanić
In this paper we introduce a constructive approach to study well-posedness of solutions to stochastic fluid-structure interaction with stochastic noise. We focus on a benchmark pro…
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…
Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid-structure interaction
Jeffrey Kuan, Tadahiro Oh, Sunčica Čanić
We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid-structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear e…
Regularity comparison of symbolic powers, integral closure of powers and powers of edge ideals
Arvind Kumar, Rajiv Kumar
We study the regularity of small symbolic powers and integral closure of small powers of edge ideals. We also prove that the regularity of integral closure of powers of edge ideals…
A stochastically perturbed fluid-structure interaction problem modeled by a stochastic viscous wave equation
Jeffrey Kuan, Suncica Canic
We study well-posedness for fluid-structure interaction driven by stochastic forcing. This is of particular interest in real-life applications where forcing and/or data have a stro…
Deterministic ill-posedness and probabilistic well-posedness of the viscous nonlinear wave equation describing fluid-structure interaction
Jeffrey Kuan, Suncica Canic
We study low regularity behavior of the nonlinear wave equation in augmented by the viscous dissipative effects described by the Dirichlet-Neumann operator. Problems…
Stochastic Baxterisation of a fused Hecke algebra
Jeffrey Kuan
Baxterisation is a procedure which constructs solutions of the Yang-Baxter equation from algebra representations. A recent paper arXiv:2004.05035 provides Baxterisation formulas fo…
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-…
Coxeter Group Actions on Interacting Particle Systems
Jeffrey Kuan
We provide a conceptual proof of the color-position symmetry of colored ASEP by relating it to the actions of Coxeter groups. The group action (and hence the color-position symmetr…
Algebraic Symmetry and Self-Duality of an Open ASEP
Jeffrey Kuan
We consider the asymmetric simple exclusion process (ASEP) with open boundary condition at the left boundary, where particles exit at rate γ and enter at rate α = γτ^2, and where τ…