The paper proves convergence of renormalised models in regularity structures for variable coefficient singular SPDEs across full subcritical regimes, with renormalisation functions depending only on a finite jet of the coefficient field.
Anderson stochastic quantization equation
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abstract
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity. After renormalizing the nonlinearity, we construct the random Gibbs measure as an absolutely continuous measure with respect to the law of the Anderson Gaussian Free Field for fixed realization of the spatial white noise. Then, when the initial data is distributed according to the Gibbs measure, we prove almost sure global well-posedness for the dynamics and invariance of the Gibbs measure.
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Renormalised Models for Variable Coefficient Singular SPDEs
The paper proves convergence of renormalised models in regularity structures for variable coefficient singular SPDEs across full subcritical regimes, with renormalisation functions depending only on a finite jet of the coefficient field.