Convergence problems for singular stochastic dynamics.

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• Younes Zine, University of Edinburgh
• Monday 14 November 2022, 16:00-17:00
• WATN-LT B (101).

If you have a question about this talk, please contact Yuzhao Wang.

Over the last twenty years there has been significant progress in the well-posedness study of singular stochastic PDEs in both parabolic and dispersive settings. In this talk, I will discuss some convergence problems for singular stochastic nonlinear PDEs. In a seminal work, Da Prato and Debussche (2003) established well-posedness of the stochastic quantization equation, also known as the parabolic Φk+12-model in the two-dimensional case. More recently, Gubinelli, Koch, Oh, and Tolomeo proved the corresponding well-posedness for the canonical stochastic quantization equation, also known as the hyperbolic Φk+12-model in the two-dimensional case. In the first part of this talk, I will describe convergence of the hyperbolic Φk+12-model to the parabolic Φk+12-model. In the dispersive setting, Bourgain (1996) established well-posedness for the dispersive Φ42-model (=deterministic cubic nonlinear Schrödinger equation) on the two-dimensional torus with Gibbsian initial data. In the second part of the talk, I will discuss the convergence of the stochastic complex Ginzburg-Landau equation (= complex-valued version of the parabolic Φ42-model) to the dispersive Φ42-model at statistical equilibrium.

This talk is part of the Analysis seminar series.

This talk is included in these lists:

• Analysis seminar
• School of Mathematics events
• WATN-LT B (101)

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