Invariant Gibbs measure for Anderson NLW

Zachhuber Immanuel, FU Berlin

We study the Gaussian measure whose covariance is related to the Anderson Hamiltonian operator, proving that it admits a regular coupling to the (standard) Gaussian free field exploiting the stochastic optimal control formulation of Gibbs measures. Using this coupling we define the renormalised powers of the Anderson free field and we prove that the associated quartic Gibbs measure is invariant under the flow of a nonlinear wave equation with renormalised cubic nonlinearity. Based on joint work with Nikolay Barashkov and Francesco De Vecchi

Area: CS33 - Measures, optimal transport and quantum systems (Francesco De Vecchi)

Keywords: SPDE Gaussian measure wave equation

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