Moments of the SHE under delta initial measure
arXiv:1808.04353
Abstract
We give a rigorous proof of the contour integral formulas of the moments of the stochastic heat equation (SHE) started from the delta initial measure at the origin. These formulas were conjectured in [BC14] (see also [CDR10, Dot10]). Our proof is based on a correspondence between the SHE and the Airy point process which was proved in [BG16, Theorem 1] using the formula of [ACQ11, Theorem 1.1].
arXiv comment16 pages
References in corpus (12)
- Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
- Free-energy distribution of the directed polymer at high temperature
- Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
- The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1
- The Continuum Directed Random Polymer
- Random-walk in Beta-distributed random environment
- Coulomb-gas electrostatics controls large fluctuations of the KPZ equation
- The ASEP and determinantal point processes
- Moments Match between the KPZ Equation and the Airy Point Process
- Intermediate disorder limits for multi-layer semi-discrete directed polymers
- Kardar-Parisi-Zhang equation and large deviations for random walks in weak random environments
- The KPZ equation and moments of random matrices