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Explore fermionic stochastic analysis through Grassmann random variables in this 46-minute mathematical lecture. Discover how these variables enable stochastic quantization of Euclidean fermionic quantum field theories, building on foundational work by Osterwalder and Schrader. Learn about essential stochastic analytical tools including Grassmann Brownian motion and non-commutative $L^p$ spaces, implemented through non-commutative analysis techniques. Examine practical applications of these mathematical frameworks and gain insights from collaborative research with F. De Vecchi, L. Fresta and M. Gubinelli in this advanced presentation on the intersection of stochastic processes and quantum field theory.
