Markov Chains, Products of Random Matrices, and the Main Problem of Modern Eschatology
2012, v.18, №2, 341-353
It is well-known that the Gauss curvature of two-dimensional geodesic surfaces in the Universe is not constant. Theoretically, this might systematically distort some results of cosmological tests designed to evaluate the final fate of the Universe: will it disperse or collapse? Up to now, it is not clear if this possible distortion could really affect cosmological observations. In the present paper some mathematical models related to Markov chains, products of random matrices and diffusion processes are discussed, in order to help with the estimation of possible distortions due to curvature variation influence.
Keywords: random curvature,Markov chains,Furstenberg's theory,Lyapunovexponents,Jacobi fields,conjugate points