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Moments of the SHE under delta initial measure

Probability 2018-10-17 v2 Mathematical Physics math.MP

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].

Keywords

Cite

@article{arxiv.1808.04353,
  title  = {Moments of the SHE under delta initial measure},
  author = {Promit Ghosal},
  journal= {arXiv preprint arXiv:1808.04353},
  year   = {2018}
}

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16 pages