Stochastic quantization of the $\Phi^3_3$-model

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(Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here.

• See the abstract in the paper.) We study the construction of the $\Phi^3_3$-measure and complete the program on the (non-)construction of the focusing Gibbs measures, initiated by Lebowitz, Rose, and Speer (1988).
• This problem turns out to be critical, exhibiting the following phase transition.
• In the weakly nonlinear regime, we prove normalizability of the $\Phi^3_3$-measure and show that it is singular with respect to the massive Gaussian free field.