Short Time Large Deviations of the KPZ Equation

Yier Lin, Li Cheng Tsai

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 small parameter ε to the noise, and establish an LDP for the trajectory of the solution. Such a Freidlin–Wentzell LDP gives the short-time, one-point LDP for the KPZ equation in terms of a variational problem. Analyzing this variational problem under the narrow wedge initial data, we prove a quadratic law for the near-center tail and a 52 law for the deep lower tail. These power laws confirm existing physics predictions (Kolokolov and Korshunov in Phys Rev B 75(14):140201, 2007, Phys Rev E 80(3):031107, 2009; Meerson et al. in Phys Rev Lett 116(7):070601, 2016; Le Doussal et al. in Phys Rev Lett 117(7):070403, 2016; Kamenev et al. in Phys Rev E 94(3):032108, 2016).

Original languageEnglish (US)
Pages (from-to)359-393
Number of pages35
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Aug 2021

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Short Time Large Deviations of the KPZ Equation'. Together they form a unique fingerprint.

Cite this