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### Moment Formula for the Stochastic Heat Equation (SHE) with Multiplicative Noise. on a Ring

**Mathematical Physics & Probability**

Speaker: | Axel Saenz |

Related Webpage: | https://sites.google.com/view/axelsaenz/home |

Location: | 1147 MSB |

Start time: | Wed, Mar 11 2020, 4:10PM |

We take the SHE with multiplicative noise on a one dimensional ring and compute the second moment, and we look at both cases for discrete or continuous space. For the different cases, we compute the second moment of the SHE with multiplicative noise via distinct methods. For the discrete case, we use a contour integral formula inspired by a similar contour integral formula appearing in the work of Tracy-Widom (2007) for the asymmetric simple exclusion process and it generalizes results of Borodin-Corwin (2014) for SHE on the line. For the continuous case, we use a Picard iterative scheme inspired by the work of Chen-Dalang (2015) for SHE on the line. This is based on joint work with Le Chen from Emory University.