Lyapunov Exponents of the Half-Line SHE

@article{Lin2020LyapunovEO,
  title={Lyapunov Exponents of the Half-Line SHE},
  author={Yier Lin},
  journal={arXiv: Probability},
  year={2020}
}
  • Yier Lin
  • Published 20 July 2020
  • Mathematics
  • arXiv: Probability
We consider the half-line stochastic heat equation (SHE) with Robin boundary parameter $A = -\frac{1}{2}$. Under narrow wedge initial condition, we compute every positive (including non-integer) Lyapunov exponents of the half-line SHE. As a consequence, we prove a large deviation principle for the upper tail of the half-line KPZ equation under Neumann boundary parameter $A = -\frac{1}{2}$ with rate function $\Phi_+^{\text{hf}} (s) = \frac{2}{3} s^{\frac{3}{2}}$. This confirms the prediction of… 
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