 

Gabriel C. DrummondCole and John Terilla
Homotopy probability theory on a Riemannian manifold and the Euler equation view print


Published: 
August 22, 2017

Keywords: 
probability, fluids, Riemannian manifolds, homotopy 
Subject: 
55U35, 58Axx, 58Cxx, 60Axx, 76xx 


Abstract
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 homotopy probability theory to study fluid flow are introduced.


Acknowledgements
The first author was supported by IBSR003D1


Author information
Gabriel C. DrummondCole:
Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Republic of Korea 37673
gabriel@ibs.re.kr
John Terilla:
Department of Mathematics, The Graduate Center and Queens College, The City University of New York, USA
jterilla@gc.cuny.edu

