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

本研究从概率论、分析学、图论、数论和计算机科学等主要领域出发，通过对无穷维随机分析的研究，探讨了量子化和量子信息分析的新途径。特别是在二阶微分的高阶塞萨罗定义的奇异拉普拉斯算子的随机分析基础上，成功地建立了白色噪声的高阶导数理论。在这个方向上建立量子信息分析是一个相当重要的进展和创新点。

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.