Hao Shen

activity

20182021

most citedSome recent progress in singular stochastic PDEs

10 citations · 11 across the 2 of their papers we have counts for

collaborators

Showing math.PRShow all

8 papers · 1 filter

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

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

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

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…