About

My research focuses on stochastic partial differential equations (SPDEs), stochastic analysis, mathematical physics and Dirichlet form theory. Currently, I am mainly working on stochastic partial differential equations with singular noise and stochastic fluid equations; stochastic quantization and quantum many body.

Stochastic Analysis
SPDEs
Singular SPDEs
Stochastic Quantization
SPDEs in Fluid Dynamics
Dirichlet Forms
Quantum Many Body
Quantum Field Theory
Mathematical Physics
KPZ Equations
Stochastic Navier-Stokes
Stochastic Euler Equations

Publications

Stochastic Quantization and Quantum Fields

  • Makeenko-Migdal equations for lattice Yang-Mills-Higgs
    with Hao Shen, Scott Andrew Smith
    arXiv preprint
    arXiv:2512.00570
  • Large N limit of the Langevin dynamics for the spin O(N) model
    with Wenjie Ye
    arXiv preprint
    arXiv:2509.13817
  • Φ43 Theory from many-body quantum Gibbs states
    with Phan Thành Nam, Xiangchan Zhu
    arXiv preprint
    arXiv:2502.04884
  • Makeenko-Migdal equations for 2D Yang-Mills: from lattice to continuum
    with Hao Shen, Scott A. Smith
    arXiv preprint
    arXiv:2412.15422
  • Langevin dynamics of lattice Yang-Mills-Higgs and applications
    with Hao Shen, Xiangchan Zhu
    To appear in Communications in Mathematical Physics
    arXiv
  • Large N limit and 1/N expansion of invariant observables in O(N) linear σ-model via SPDE
    with Hao Shen, Xiangchan Zhu
    Probability Theory and Related Fields, 191, 2025, no.3-4, 853-932
    arXiv
  • A new derivation of the finite N master loop equation for lattice Yang-Mills
    with Hao Shen, Scott Smith
    Electron. J. Probab. 29 no. 29, 1--18, 2024
    arXiv
  • A Stochastic Analysis Approach to Lattice Yang-Mills at Strong Coupling
    with Hao Shen, Xiangchan Zhu
    Communications in Mathematical Physics, 400 (2023), no. 2, 805--851
    arXiv
  • An SPDE approach to perturbation theory of Φ42: asymptoticity and short distance behavior
    with Hao Shen, Xiangchan Zhu
    The Annals of Applied Probability, 33(4): 2600-2642, 2023
    arXiv
  • Large N Limit of the O(N) Linear Sigma Model in 3D
    with Hao Shen, Xiangchan Zhu
    Communications in Mathematical Physics, 394 no.3, 953--1009, 2022
    arXiv
  • Large N Limit of the O(N) Linear Sigma Model via Stochastic Quantization
    with Hao Shen, Scott Smith, Xiangchan Zhu
    The Annals of Probability, 50(1), 131-202, 2022
    arXiv
  • Dirichlet form associated with the Φ43 model
    with Xiangchan Zhu
    Electron. J. Probab. 23, no. 78, 1-31, 2018
    arXiv
  • Lattice approximation to the dynamical Φ43 model
    with Xiangchan Zhu
    Ann. Probab. 46 no. 1, 397-455, 2018
    arXiv
  • Ergodicity for the Stochastic Quantization Problems on the 2D-Torus
    with Michael Röckner, Xiangchan Zhu
    Comm. Math. Phys. 352 no. 3, 1061--1090, 2017
    arXiv
  • Restricted Markov uniqueness for the stochastic quantization of P(Φ)2 and its applications
    with Michael Röckner, Xiangchan Zhu
    J. Funct. Anal. 272 no. 10, 4263-4303, 2017
    arXiv

Stochastic Fluid Dynamics

  • A proof of Onsager's conjecture for the stochastic 3D Euler equations
    with Huaxiang Lü, Lin Lü
    arXiv preprint
    arXiv:2505.06915
  • Non-unique ergodicity for deterministic and stochastic 3D Navier-Stokes and Euler equations
    with Martina Hofmanová, Xiangchan Zhu
    Archive for Rational Mechanics and Analysis, (2025) 249:33
    arXiv
  • Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations
    with Martina Hofmanová, Umberto Pappalettera, Xiangchan Zhu
    The Annals of applied probability, 35(5): 3119-3149
    arXiv
  • Non-uniqueness of Leray-Hopf solutions for stochastic forced Navier-Stokes equations
    with Martina Hofmanová, Xiangchan Zhu
    Electron. J. Probab. 29 (2024) 195, 1-27
    arXiv
  • Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise
    with Martina Hofmanová, Xiaoyutao Luo, Xiangchan Zhu
    Mathematische Annalen 390:5111-5152, 2024
    arXiv
  • A class of supercritical/critical singular stochastic PDEs: Existence, non-uniqueness, non-Gaussianity, non-unique ergodicity
    with Martina Hofmanová, Xiangchan Zhu
    J. Funct. Anal. 285(2023), no. 5, Paper No. 110011
    arXiv
  • Non-uniqueness in law of stochastic 3D Navier-Stokes equations
    with Martina Hofmanová, Xiangchan Zhu
    J. Eur. Math. Soc. 26, 163--260 (2024)
    arXiv
  • Global existence and non-uniqueness for 3D Navier-Stokes equations with space-time white noise
    with Martina Hofmanová, Xiangchan Zhu
    Archive for Rational Mechanics and Analysis, 247 (2023), no. 3, Paper No. 46
    arXiv
  • Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier-Stokes equations: existence and non-uniqueness
    with Martina Hofmanová, Xiangchan Zhu
    The Annals of Probability, 2023, Vol. 51, No. 2, 524-579
    arXiv
  • On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
    with Martina Hofmanová, Xiangchan Zhu
    Commun. Pure Appl. Math. Vol. LXXV, 2446--2510 (2022)
    arXiv
  • Random attractor associated with the quasi-geostrophic equation
    with Xiangchan Zhu
    J. Dynam. Differential Equations 29, no. 1, 289--322, 2017
    arXiv
  • Three dimensional Navier-Stokes equation driven by space-time white noise
    with Xiangchan Zhu
    Journal of Differential Equations, 259, 4443--4508, 2015
    arXiv
  • Sub- and supercritical stochastic quasi-geostrophic equation
    with Michael Röckner, Xiangchan Zhu
    The Annals of Probability, 43, No. 3, 1202--1273, 2015
    arXiv
  • Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise
    with Michael Röckner, Xiangchan Zhu
    Stochastic Processes and their Applications, 124 1974--2002, 2014
    arXiv

General Theory of SPDEs

  • Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus
    with Hao Shen, Xiangchan Zhu
    To appear in Stochastics and Partial Differential Equations: Analysis and Computations
    arXiv
  • Singular kinetic equations and applications
    with Zimo Hao, Xicheng Zhang, Xiangchan Zhu
    The Annals of Probability Vol. 52, No. 2, 576--657, 2024
    arXiv
  • Gaussian fluctuations for interacting particle systems with singular kernels
    with Zhenfu Wang, Xianliang Zhao
    Archive for Rational Mechanics and Analysis, (2023) 247:101
    arXiv
  • Singular HJB equations with applications to KPZ on the real line
    with Xicheng Zhang, Xiangchan Zhu
    Probability Theory and Related Fields, 183 no. 3-4, 789--869, 2022
    arXiv
  • Conservative stochastic 2-dimensional Cahn-Hilliard equation
    with Michael Röckner, Huanyu Yang
    The Annals of Applied Probability, Vol. 31, No. 3, 1336-1375, 2021
    arXiv
  • Stochastic heat equation for infinite string with values in manifold
    with Xin Chen, Bo Wu, Xiangchan Zhu
    Transactions of the American Mathematical Society, 374(1):407-452, 2021
    arXiv
  • Stochastic Heat Equations with Values in a Manifold via Dirichlet Forms
    with Michael Röckner, Bo Wu, Xiangchan Zhu
    SIAM J. Math. Anal., 52(3):2237-2274, 2020
    arXiv
  • The stochastic reflection problem on a convex set of a Hilbert space and BV functions in a Gelfand triple
    with Michael Röckner, Xiangchan Zhu
    The Annals of Probability, 40, 1759-1794, 2012
    arXiv