Jeffrey Kuan

Department of Mathematics
Texas A&M University
Blocker Building, Room 525L
College Station, TX 77843
Email: jkuan(at)


Asymptotics of dynamic ASEP (with Zhengye Zhou), in preparation.

An explicit central element of Uq(so5) and its corresponding quantum Hamiltonian, preprint.

Orthogonal Dualities and Asymptotics of Dynamic Stochastic Higher Spin Vertex Models through Drinfeld Twister (with Zhengye Zhou), submitted to Probability and Mathematical Physics.

Asymptotics of two-point correlations in the multi-species q-TAZRP (with Zhengye Zhou*), submitted to Brazilian Journal of Probability and Statistics.

Orthogonal Polynomial Duality for Type D ASEP (with Danyil Blyschak, Olivia Burke, Dennis Li, Sasha Ustilovsky and Zhengye Zhou), to appear in Journal of Statistical Physics.

Orthogonal polynomial duality and unitary symmetries of multi–species ASEP(q;θ) and higher–spin vertex models via  *-bialgebra structure of higher rank quantum groups (with Chiara Franceschini and Zhengye Zhou), submitted to Communications in Mathe-matical Physics.

Joint q-moments and shift invariance for the multi-species q-TAZRP on the infinite line, to appear in Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions.

Three-dimensional Gaussian fluctuations of spectra of overlapping stochastic Wishart matrices (with Zhengye Zhou), to appear in Random Matrices: Theory and Applications.

Stochastic Baxterisation of a fused Hecke algebra, Communications in Algebra..

Interacting particle systems with type D symmetry and duality (with Mark Landry, Andrew Lin, Andrew Park, Zhengye Zhou), Houston Journal of Mathematics, Volume 48, Number 3, 2022, Pages 499–538..

Determinantal expressions in multi-species TASEP, SIGMA 16 (2020), 133, 6 pages.

Two dualities: Markov and Schur-Weyl. to appear in International Mathematics Research Notices.

Coxeter Group Actions on Interacting Particle Systems, Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 397-410 (August 2022).

Algebraic Symmetry and Self-Duality of an Open ASEP, Math Phys Anal Geom24, 12 (2021).

A Short Note on Markov Duality in Multi-species Higher Spin Stochastic Vertex Models, to appear in Electronic Communications in Probability.

Stochastic Fusion of Interacting Particle Systems and Duality Functions, to appear in Annales de l’Institut Henri Poincaré (B).

Explicit central elements of Uq(gln), to appear in SIGMA.

Probability distributions of multi-species q-TAZRP and ASEP as double cosets of parabolic subgroups, Annales Henri Poincaré , April 2019, 20(4), 1149-1173

An algebraic construction of duality functions for the stochastic Uq(An(1)) vertex model and its degenerations, Communications in Mathematical Physics, 359(1):121–187, Apr 2018.

Hard-edge asymptotics of the Jacobi growth process (with Mark Cerenzia), Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 56, Number 4, November 2020, pages 2329-2355..

A multi-species ASEP(q,j) and q-TAZRP with stochastic duality, International Mathematics Research Notices, 2018(17):5378–5416, 2018.

An interacting particle system with geometric jump rates near a partially reflecting boundary, Electronic Communications in Probability, Volume 21 (2016), paper no. 76, 15 pp.

A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups, submitted to Journal of Mathematical Physics.

Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two, Journal of Physics A, Mathematical and Theoretical , Volume 49, Number 11 (2016), 29 pp.

Three-dimensional Gaussian fluctuations of non-commutative random surfaces along time-like paths, Advances in Mathematics, Volume 303, 5 November 2016, Pages 716–744.

Two constructions of Markov chains on the dual of U(n), Journal of Theoretical Probability Volume 31, Pages 1411–1428 (2018).

Strong Szego asymptotics and zeros of the zeta-function (with Paul Bourgade), Communications on Pure and Applied Mathematics, Volume 67, Issue 6, 1028–1044, June 2014.

Asymptotics of a discrete-time particle system near a reflecting boundary, Journal of Statistical Physics , Volume 150, Issue 2 (2013), Pages 398-411.

The Gaussian free field in interlacing particle systems, Electronic Journal of Probability 19 (2014), no. 72, 1-31.

Random surface growth with a wall and Plancherel measures for O(infinity) (with Alexei Borodin), Communications on Pure and Applied Mathematics, Volume 63, Issue 7, July 2010, Pages 831-894.

Asymptotics of Plancherel measures for the infinite-dimensional unitary group (with Alexei Borodin),
Advances in Mathematics, Volume 219, Issue 3, 20 October 2008, Pages 894–931.