Generalizations of infinite dimensional Laplacians, construction methods of stochastic processes and developments in quantum information analysis

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In this research, we considered a quantization and a new approach to a quantum information analysis by researching the infinite dimensional stochastic analysis jointly from major fields : probability theory, analysis, graph theory, number theory and computer science. Especially we succeeded in constructing the theory of higher order derivatives of white noise based on the stochastic analysis associated with exotic Laplacians defined by higher order Cesaro means of the second differentiation. It is a quite important progress and a creative point that a quantum information analysis in this direction can be constructed.