10 papers
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…
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…