Riemann Manifold Diffusion Simplifies Path Integral Construction

Paolo Muratore-Ginanneschi of the University of Helsinki, Department of Mathematics and Statistics, simplified the construction of path integrals by leveraging a specific mathematical representation of diffusion processes. The researcher’s work centers on diffusion generated by state-dependent noise, also known as multiplicative noise, a phenomenon crucial to investigating non-equilibrium statistical physics. Muratore-Ginanneschi utilizes the Belopol’skaya-Daletskii formulation to build equivariant representations of these diffusion path measures, offering a way to create finite-dimensional approximations to previously complex calculations. The key ingredient is the use of the exponential map to describe the increments of the diffusion, providing an elementary method for this construction. Mapping Chaos: A New Route to Understanding Diffusion on Complex Surfaces The seemingly intractable problem of accurately modeling…