Stochastic Analysis and Quantum Fields

Explore the intersection of stochastic analysis and quantum fields in this comprehensive lecture from the Hausdorff Junior Trimester Program on Randomness, PDEs, and Nonlinear Fluctuations. Delve into recent advancements in understanding singular SPDEs that describe large-scale non-linear fluctuations of particle systems. Examine the relevance of these equations to the construction of Euclidean quantum fields through stochastic quantization. Review the various implementations of stochastic quantization and investigate how stochastic analysis can be applied to construct and analyze Euclidean quantum fields. Gain insights into the cutting-edge research connecting stochastic processes and quantum field theory in this hour-long presentation by Massimiliano Gubinelli.