Email: pkushenhao at gmail
Short bio: I obtained my PhD from Princeton in 2013. Since then, I worked as a postdoc at Warwick, a Ritt Assistant Professor at Columbia, and was a faculty member at UW-Madison before joining University of Chicago in 2026.
I am interested in stochastic analysis, stochastic PDE, and various topics on mathematical physics.
A survey:
Some recent progress in singular stochastic partial differential equations. (with I. Corwin) Bulletin of the AMS (2020). arxiv:1904.00334 (journal)
Quantization of Yang-Mills and other gauge theories:
Stochastic quantization of an abelian gauge theory. Comm. Math. Phys. (2021). arXiv:1801.04596
Langevin dynamic for the 2D Yang-Mills measure. (with A. Chandra, I. Chevyrev, M. Hairer) Publ. Math. IHÉS. (2022). arXiv:2006.04987
Stochastic quantisation of Yang-Mills-Higgs in 3D. (with A. Chandra, I. Chevyrev, M. Hairer) Inventiones. (2024). arXiv:2201.03487
A new derivation of the finite N master loop equation for lattice Yang-Mills. (with S. Smith, R. Zhu) EJP (2024). arXiv:2202.00880
A stochastic analysis approach to lattice Yang-Mills at strong coupling. (with R. Zhu, X. Zhu) Comm. Math. Phys. arXiv:2204.12737
Invariant measure and universality of the 2D Yang-Mills Langevin dynamic. (with I. Chevyrev) CPAM. arXiv:2302.12160
Langevin dynamics of lattice Yang-Mills-Higgs and applications. (with R. Zhu, X. Zhu) Comm. Math. Phys. (2026). arXiv:2401.13299
Makeenko-Migdal equations for 2D Yang-Mills: from lattice to continuum. (with S. Smith, R. Zhu). arXiv:2412.15422
Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs. (with I. Chevyrev) ARMA (2026). arXiv:2503.03060
Makeenko-Migdal equations for lattice Yang-Mills-Higgs. (with S. Smith, R. Zhu). arXiv:2512.00570
Singular SPDE in critical dimensions:
The four-dimensional Anderson model: a case study for critical SPDEs. (with Y. Deng). arXiv:2607.10105
Stochastic PDE related with other quantum field theory problems:
A stochastic PDE approach to large N problems in quantum field theory: a survey. J. Math. Phys. (2022) arXiv:2208.02381
An SPDE approach to perturbation theory of Φ42: asymptoticity and short distance behavior. (with R. Zhu, X. Zhu). Ann. Appl. Prob. (2022) arXiv:2108.11312
Large N limit of the O(N) linear sigma model via stochastic quantization. (with S. Smith, R. Zhu, X. Zhu) Ann. Probab. (2022). arXiv:2005.09279
Large N limit of the O(N) linear sigma model in 3D. (with R. Zhu, X. Zhu) Comm. Math. Phys. (2022). arXiv:2102.02628
Large N limit and 1/N expansion of invariant observables in O(N) linear σ-model via SPDE. (with R. Zhu, X. Zhu) PTRF. (2025). arXiv:2306.05166
Stochastic Ricci Flow on Compact Surfaces. (with J. Dubédat) Int. Math. Res. Not. (2021). arXiv:1904.10909
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. (with W. E and A. Jentzen) (2013) Nonlinear Analysis. arXiv:1302.5930
Soliton problems:
Concentration and fluctuations of sine-Gordon measure around topological multi-soliton manifold (with K. Seong, P. Sosoe) (2025). arXiv:2512.23957
Gobal well-posedness problems:
Global well-posedness for generalized parabolic Anderson model on the whole plane (with R. Zhu, X. Zhu) arxiv:2606.26681
Global well-posedness for 2D generalized parabolic Anderson model via paracontrolled calculus. (with R. Zhu, X. Zhu) Stoch PDE: Anal Comp. (2025). arXiv:2402.19137
More papers on regularity structures (KPZ, stochastic quantization, weak universality etc.)
A central limit theorem for the KPZ equation. (with M. Hairer) Ann. Probab. (2017). arXiv:1507.01237
The dynamical sine-Gordon model. (with M. Hairer) Comm. Math. Phys. (2016). arXiv:1409.5724
Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem. (with A. Chandra) EJP (2017). arXiv:1605.05683
Weak universality of dynamical Φ43: non-Gaussian noise. (with W. Xu) Stoch PDE: Anal Comp. (2018). arXiv:1601.05724
Local solution to the multi-layer KPZ equation. (with A. Chandra and D. Erhard), J. Stat. Phys. (2019). arXiv:1901.00882
The dynamical sine-Gordon model in the full subcritical regime. (with A. Chandra and M. Hairer) (2018) arXiv:1808.02594
Stochastic PDE limits of statistical physics models:
ASEP(q,j) converges to the KPZ equation. (with I. Corwin and L-C. Tsai) (2016) AIHP (B) Probab. Stat. arXiv:1602.01908
Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits. (with H. Weber) J. Funct. Anal. (2018). arXiv:1608.06556
Open ASEP in the weakly asymmetric regime. (with I. Corwin) CPAM (2018). arXiv:1610.04931
Stochastic PDE limit of the six vertex model. (with I. Corwin, P. Ghosal and L-C. Tsai). Comm. Math. Phys. (2020). arXiv:1803.08120
Stochastic Telegraph equation limit for the stochastic six vertex model. (with L-C. Tsai) Proc. Amer. Math. Soc. (2019). arXiv:1807.04678
Scaling limit of a directed polymer among a Poisson field of independent walks. (with J. Song, R. Sun, L. Xu), J. Funct. Anal. (2021). arXiv:2003.12945
Mean field limit of a dynamical model of polymer systems. (with W. E) Sci. China Math. (2013).
Integrable probability:
The strict-weak lattice polymer. (with I. Corwin and T. Seppäläinen) J. Stat. Phys. (2015). arXiv:1409.1794
Rigorous renormalization group analysis:
Exact renormalization group analysis of turbulent transport by the shear flow. (with W. E) J. Stat. Phys. (2013). arXiv:1307.6000
A renormalization group method by harmonic extensions and the classical dipole gas. Ann. Henri Poincaré, (2016). arXiv:1311.2305