Hao Shen

activity

20132026

most citedThe dynamical sine-Gordon model

86 citations · 384 across the 29 of their papers we have counts for

collaborators

30 papers

math.PR2026

Scaling limit of the 3D abelian Yang--Mills Langevin dynamics

Ilya Chevyrev, Yahui Qu, Hao Shen

We study the continuum scaling limit of the Langevin dynamics for three-dimensional U(1) lattice Yang--Mills theory. The model is defined on the discrete 3D torus with a general cl…

math.PR2023★ 1 cited

Large $N$ limit and $1/ N$ expansion of invariant observables in $O (N)$ linear $σ$ -model via SPDE

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper, we continue the study of large $N$ problems for the Wick renormalized linear sigma model, i.e. $N$ -component $Φ^{4}$ model, in two spatial dimensions, using stochastic…

math.PR2023★ 3 cited

Invariant measure and universality of the 2D Yang-Mills Langevin dynamic

Ilya Chevyrev, Hao Shen

We prove that the Yang-Mills (YM) measure for the trivial principal bundle over the two-dimensional torus, with any connected, compact structure group, is invariant for the associa…

math.PR2022★ 5 cited

A stochastic PDE approach to large N problems in quantum field theory: a survey

Hao Shen

In this survey we review some recent rigorous results on large N problems in quantum field theory, stochastic quantization and singular stochastic PDEs, and their mean field limit…

math.PR2022★ 12 cited

A stochastic analysis approach to lattice Yang--Mills at strong coupling

Hao Shen, Rongchan Zhu, Xiangchan Zhu

We develop a new stochastic analysis approach to the lattice Yang--Mills model at strong coupling in any dimension $d > 1$ , with t' Hooft scaling $β N$ for the inverse coupling streng…

math.PR2022★ 2 cited

A new derivation of the finite $N$ master loop equation for lattice Yang-Mills

Hao Shen, Scott A. Smith, Rongchan Zhu

We give a new derivation of the finite $N$ master loop equation for lattice Yang-Mills theory with structure group $S O (N)$ , $U (N)$ or $S U (N)$ . The $S O (N)$ case was initially proved…

math.PR2022★ 23 cited

Stochastic quantisation of Yang-Mills-Higgs in 3D

Ajay Chandra, Ilya Chevyrev, Martin Hairer +1

We define a state space and a Markov process associated to the stochastic quantisation equation of Yang-Mills-Higgs (YMH) theories. The state space $S$ is a nonlinear met…

math.PR2021★ 3 cited

An SPDE approach to perturbation theory of $Φ_{2}^{4}$ : asymptoticity and short distance behavior

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper we study the perturbation theory of $Φ_{2}^{4}$ model on the whole plane via stochastic quantization. We use integration by parts formula (i.e. Dyson-Schwinger equations)…

math.PR2021★ 13 cited

Large $N$ limit of the $O (N)$ linear sigma model in 3D

Hao Shen, Rongchan Zhu, Xiangchan Zhu

In this paper we study the large N limit of the $O (N)$ -invariant linear sigma model, which is a vector-valued generalization of the $Φ^{4}$ quantum field theory, on the three dimensi…

hep-ph2021★ 3 cited

Gauge invariance of the vector meson mass in the Coleman-Weinberg model

Haojie Shen, Yu Cheng, Wei Liao

We revisit the problem of the gauge invariance in the Coleman-Weinberg model in which a $U (1)$ gauge symmetry is driven spontaneously broken by radiative corrections. It was notice…

math.PR2020★ 54 cited

Langevin dynamic for the 2D Yang-Mills measure

Ajay Chandra, Ilya Chevyrev, Martin Hairer +1

We define a natural state space and Markov process associated to the stochastic Yang-Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributio…

math.PR2020

Large $N$ Limit of the $O (N)$ Linear Sigma Model via Stochastic Quantization

Hao Shen, Scott Smith, Rongchan Zhu +1

This article studies large $N$ limits of a coupled system of $N$ interacting $Φ^{4}$ equations posed over $T^{d}$ for $d = 2$ , known as the $O (N)$ linear sigma model. Uniform…

math.PR2020★ 1 cited

Scaling limit of a directed polymer among a Poisson field of independent walks

Hao Shen, Jian Song, Rongfeng Sun +1

We consider a directed polymer model in dimension $1 + 1$ , where the disorder is given by the occupation field of a Poisson system of independent random walks on $Z$ . In a su…

math.PR2019★ 10 cited

Stochastic Ricci Flow on Compact Surfaces

Julien Dubédat, Hao Shen

In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow is symmetric with respect to a measure induced by Liouville Conformal Field Theory. U…

math.PR2019★ 10 cited

Some recent progress in singular stochastic PDEs

Ivan Corwin, Hao Shen

Stochastic PDEs are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent progress in d…

math.PR2019★ 1 cited

Local solution to the multi-layer KPZ equation

Ajay Chandra, Dirk Erhard, Hao Shen

In this article we prove local well-posedness of the system of equations $\partial_{t} h_{i} = \sum_{j = 1}^{i} \partial_{x}^{2} h_{i} + (\partial_{x} h_{i})^{2} + ξ$ on the circle where $1\leq i…

math.PR2018★ 28 cited

The dynamical sine-Gordon model in the full subcritical regime

Ajay Chandra, Martin Hairer, Hao Shen

We prove that the dynamical sine-Gordon equation on the two dimensional torus introduced in [HS16] is locally well-posed for the entire subcritical regime. At first glance this equ…

math.PR2018★ 4 cited

Stochastic Telegraph Equation Limit for the Stochastic Six Vertex Model

Hao Shen, Li-Cheng Tsai

In this article we study the stochastic six vertex model under the scaling proposed by Borodin and Gorin (2018), where the weights of corner-shape vertices are tuned to zero, and p…

math.PR2018

Stochastic PDE Limit of the Six Vertex Model

Ivan Corwin, Promit Ghosal, Hao Shen +1

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $Δ \to 1^{+}$ so as to zoom into the ferroelectric/disordered phase crit…

math.PR2018★ 4 cited

Stochastic quantization of an Abelian gauge theory

Hao Shen

We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by…

math.PR2016★ 13 cited

Open ASEP in the Weakly Asymmetric Regime

Ivan Corwin, Hao Shen

We consider ASEP on a bounded interval and on a half line with sources and sinks. On the full line, Bertini and Giacomin proved convergence under weakly asymmetric scaling of the h…

math.PR2016★ 4 cited

Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits

Hao Shen, Hendrik Weber

We study the Glauber dynamics of a two dimensional Blume-Capel model (or dilute Ising model) with Kac potential parametrized by $(β, θ)$ - the "inverse temperature" and the "chemica…

math.PR2016★ 2 cited

Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem

Ajay Chandra, Hao Shen

Upon its inception the theory of regularity structures allowed for the treatment for many semilinear perturbations of the stochastic heat equation driven by space-time white noise.…

math-ph2016★ 7 cited

Weak universality of dynamical $Φ_{3}^{4}$ : non-Gaussian noise

Hao Shen, Weijun Xu

We consider a class of continuous phase coexistence models in three spatial dimensions. The fluctuations are driven by symmetric stationary random fields with sufficient integrabil…

Scaling limit of the 3D abelian Yang--Mills Langevin dynamics

Large N limit and 1/N expansion of invariant observables in O(N) linear σ-model via SPDE

Invariant measure and universality of the 2D Yang-Mills Langevin dynamic

A stochastic PDE approach to large N problems in quantum field theory: a survey

A stochastic analysis approach to lattice Yang--Mills at strong coupling

A new derivation of the finite N master loop equation for lattice Yang-Mills

Stochastic quantisation of Yang-Mills-Higgs in 3D

An SPDE approach to perturbation theory of Φ24​: asymptoticity and short distance behavior

Large N limit of the O(N) linear sigma model in 3D

Gauge invariance of the vector meson mass in the Coleman-Weinberg model

Langevin dynamic for the 2D Yang-Mills measure

Large N Limit of the O(N) Linear Sigma Model via Stochastic Quantization

Scaling limit of a directed polymer among a Poisson field of independent walks

Stochastic Ricci Flow on Compact Surfaces

Some recent progress in singular stochastic PDEs

Local solution to the multi-layer KPZ equation

The dynamical sine-Gordon model in the full subcritical regime

Stochastic Telegraph Equation Limit for the Stochastic Six Vertex Model

Stochastic PDE Limit of the Six Vertex Model

Stochastic quantization of an Abelian gauge theory

Open ASEP in the Weakly Asymmetric Regime

Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits

Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem

Weak universality of dynamical Φ34​: non-Gaussian noise

Large $N$ limit and $1/ N$ expansion of invariant observables in $O (N)$ linear $σ$ -model via SPDE

A new derivation of the finite $N$ master loop equation for lattice Yang-Mills

An SPDE approach to perturbation theory of $Φ_{2}^{4}$ : asymptoticity and short distance behavior

Large $N$ limit of the $O (N)$ linear sigma model in 3D

Large $N$ Limit of the $O (N)$ Linear Sigma Model via Stochastic Quantization

Weak universality of dynamical $Φ_{3}^{4}$ : non-Gaussian noise