Homotopy probability theory on a Riemannian manifold and the Euler equation

Gabriel Drummond-Cole, John Terilla
2017 New York Journal of Mathematics New York J. Math   unpublished
Homotopy probability theory is a version of probability theory in which the vector space of random variables is replaced with a chain complex. A natural example extends ordinary probability theory on a finite volume Riemannian manifold M. In this example, initial conditions for fluid flow on M are identified with collections of homotopy random variables and solutions to the Euler equation are identified with homotopies between collections of homotopy random variables. Several ideas about using
more » ... ideas about using homotopy probability theory to study fluid flow are introduced.