Markov Chains, Products of Random matrices, and the Main Problem of Modern Eschatologyстатья
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Аннотация: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, Lyapunov
exponents, Jacobi fields, conjugate points