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## Infinite dimensional stochastic differential equations for Dyson’s model

- Li-Cheng Tsai
- Mathematics
- 26 May 2014

In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson’s Brownian Motion,… Expand

## Criticality of a Randomly-Driven Front

- A. Dembo, Li-Cheng Tsai
- MathematicsArchive for Rational Mechanics and Analysis
- 29 May 2017

AbstractConsider an advancing ‘front’ $${R(t) \in \mathbb{Z}_{\geqq 0}}$$R(t)∈Z≧0 and particles performing independent continuous time random walks on $${ (R(t), \infty) \cap \mathbb{Z}}$$(R(t),∞)∩Z.… Expand

## Weakly Asymmetric Non-simple Exclusion Process and the KPZ equation

- A. Dembo, Li-Cheng Tsai
- Mathematics
- 23 February 2013

## KPZ equation limit of higher-spin exclusion processes

- Ivan Corwin, Li-Cheng Tsai
- Mathematics
- 15 May 2015

We prove that under a particular weak scaling, the 4-parameter interacting particle system introduced by Corwin and Petrov converges to the KPZ equation. This expands the relatively small number of… Expand

## Stochastic PDE Limit of the Six Vertex Model

- Ivan Corwin, Promit Ghosal, Hao Shen, Li-Cheng Tsai
- MathematicsCommunications in Mathematical Physics
- 21 March 2018

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

## Coulomb-Gas Electrostatics Controls Large Fluctuations of the Kardar-Parisi-Zhang Equation.

- Ivan Corwin, Promit Ghosal, Alexandre Krajenbrink, P. Le Doussal, Li-Cheng Tsai
- MathematicsPhysical review letters
- 15 March 2018

TLDR

## ASEP(q,j) converges to the KPZ equation

- Ivan Corwin, Hao Shen, Li-Cheng Tsai
- Mathematics
- 5 February 2016

We show that a generalized Asymmetric Exclusion Process called ASEP(q,j) introduced by Carinci, Giardina, Redig and Sasamoto converges to the Cole-Hopf solution to the KPZ equation under weak… Expand

## Weakly Asymmetric Non-Simple Exclusion Process and the Kardar–Parisi–Zhang Equation

- A. Dembo, Li-Cheng Tsai
- Mathematics
- 23 February 2013

We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing the discrete Cole–Hopf transformation of Gärtner (Stoch Process Appl, 27:233–260, 1987). We… Expand

## Free Molecular Flow with Boundary Effect

- Hung-Wen Kuo, Tai-Ping Liu, Li-Cheng Tsai
- Mathematics
- 29 January 2013

We study the dissipative effect of the boundary condition in the kinetic theory. We focus our study on the simplest situation of the free molecular flow with diffuse reflection boundary condition and… Expand

## Moments of the 2D SHE at criticality

- Yu Gu, J. Quastel, Li-Cheng Tsai
- MathematicsProbability and Mathematical Physics
- 27 May 2019

We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the… Expand

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