78 citations · 349 across the 19 of their papers we have counts for
24 papers · 1 filter
Spacetime limit shapes of the KPZ equation in the upper tails
Yier Lin, Li-Cheng Tsai
We consider the -point, fixed-time large deviations of the KPZ equation with the narrow wedge initial condition. The scope consists of concave-configured, upper-tail deviations…
High moments of the SHE in the clustering regimes
Li-Cheng Tsai
We analyze the high moments of the Stochastic Heat Equation (SHE) via a transformation to the attractive Brownian Particles (BPs), which are Brownian motions interacting via pairwi…
A lower-tail limit in the weak noise theory
Yier Lin, Li-Cheng Tsai
We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle of the Stochastic Heat Equation (SHE). The logarithm of the minimizer of the va…
Large deviations of the KPZ equation via the Stochastic Airy Operator
Li-Cheng Tsai
In this article we review the ideas in Tsai (2018) toward proving the one-point, lower-tail large deviation principle for the Kardar--Parisi--Zhang equation.
Integrability in the weak noise theory
Li-Cheng Tsai
We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation (SHE). For a general class of initial-te…
KPZ equation with a small noise, deep upper tail and limit shape
Pierre Yves Gaudreau Lamarre, Yier Lin, Li-Cheng Tsai
In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter in front of the noise and let $\varepsilon \t…
Hydrodynamic large deviations of TASEP
Jeremy Quastel, Li-Cheng Tsai
We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric Simple Exclusion Process (TASEP). This problem was studied in Jensen (2000) and Varadhan (200…
Short time large deviations of the KPZ equation
Yier Lin, Li-Cheng Tsai
We establish the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a sma…
Fractional moments of the Stochastic Heat Equation
Sayan Das, Li-Cheng Tsai
Consider the solution of the one-dimensional stochastic heat equation, with a multiplicative spacetime white noise, and with the delta initial data $\mathcal{Z}(…
Moments of the 2D SHE at criticality
Yu Gu, Jeremy Quastel, Li-Cheng Tsai
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 whi…
Exact lower tail large deviations of the KPZ equation
Li-Cheng Tsai
Consider the Hopf--Cole solution of the KPZ equation with narrow wedge initial condition. Regarding as a scaling parameter, we provide the first rigorous…
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…
SPDE Limit of Weakly Inhomogeneous ASEP
Ivan Corwin, Li-Cheng Tsai
We study ASEP in a spatially inhomogeneous environment on a torus of sites. A given inhomogeneity $ \widetilde{a}(x) \in (0,\inf…
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 so as to zoom into the ferroelectric/disordered phase crit…
Exceedingly Large Deviations of the Totally Asymmetric Exclusion Process
Stefano Olla, Li-Cheng Tsai
Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice . We study the functional Large Deviations of the integrated current $ \mathsf…
Criticality of a randomly-driven front
Amir Dembo, Li-Cheng Tsai
Consider an advancing `front' and particles performing independent continuous time random walks on . Starting at $R(…
Stationary Distributions of the Atlas Model
Li-Cheng Tsai
In this article we study the Atlas model, which constitutes of Brownian particles on , independent except that the Atlas (i.e., lowest ranked) particle …
Stationary Gap Distributions for Infinite Systems of Competing Brownian Particles
Andrey Sarantsev, Li-Cheng Tsai
Consider the infinite Atlas model: a semi-infinite collection of particles driven by independent standard Brownian motions with zero drifts, except for the bottom-ranked particle w…
ASEP(q,j) converges to the KPZ equation
Ivan Corwin, Hao Shen, Li-Cheng Tsai
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…
Optimal Surviving Strategy for Drifted Brownian Motions with Absorption
Wenpin Tang, Li-Cheng Tsai
We study the 'Up the River' problem formulated by Aldous (2002), where a unit drift is distributed among a finite collection of Brownian particles on , which are an…
KPZ equation limit of higher-spin exclusion processes
Ivan Corwin, Li-Cheng Tsai
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 relativel…
Equilibrium Fluctuation of the Atlas Model
Amir Dembo, Li-Cheng Tsai
We study the fluctuation of the Atlas model, where a unit drift is assigned to the lowest ranked particle among a semi-infinite (-indexed) system of otherwise indep…
Infinite Dimensional Stochastic Differential Equations for Dyson's Model
Li-Cheng Tsai
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…
Weakly Asymmetric Non-Simple Exclusion Process and the Kardar-Parisi-Zhang Equation
Amir Dembo, Li-Cheng Tsai
We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation. We identify the main non-linearity and…