AbstractWe establish the Freidlin–Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. Analyzing this variational problem under the narrow wedge initial data, we prove a quadratic law for the near-center tail and a 5/2 law for the deep lower tail for the KPZ equation under the short time scaling.
2. Lyapunov exponents of the half-line SHE, 2020, [arXiv:2007.10212] Submitted
AbstractWe prove an upper tail large deviation of the half-line KPZ equation, with rate function to be 2/3s3/2 .
AbstractWe consider the (1+1)-dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an exact way of computing the Lyapunov exponents of the SHE for a large class of initial data which includes any bounded deterministic positive initial data and the stationary initial data. As a consequence, we derive exact formulas for the upper tail large deviation rate functions of the KPZ equation for general initial data.
AbstractIn this paper, we prove that the stochastic telegraph equation arises as a scaling limit of the stochastic higher spin six vertex (SHS6V) model with general spin I/2,J/2. This extends results of Borodin and Gorin which focused on the I=J=1 six vertex case and demonstrates the universality of the stochastic telegraph equation in this context. We also provide a functional extension of the central limit theorem obtained in [Borodin and Gorin 2019, Theorem 6.1].
AbstractWe consider the stochastic higher spin six vertex (SHS6V) model introduced in [Corwin-Petrov, 2016] with general integer spin parameters . Starting from near stationary initial condition, we prove that the SHS6V model converges to the KPZ equation under weakly asymmetric scaling.
AbstractWe prove that Schütz’s ASEP Markov duality functional is also a Markov duality functional for the stochastic six vertex model. We introduce a new method that uses induction on the number of particles to prove the Markov duality.
7. Second order behavior of the block counting process of beta coalescents (with Bastien Mallein) Electronic Communications in Probability (2017), Vol 22, no. 61, 1-8 [arXiv:1606.06998] [journal version]