Statistics of escape exponent in normal and anomalous diffusion

This paper proposes escape exponent to characterize localization or escape of moving particles, which will determine the diffusion process. So the diffusion process can also be described by the evolution of the distribution density of escape exponent with time. We studied some typical distribution density of escape exponent and discussed their properties, and an interesting phenomenon is that the escape exponent distribution of Brownian particles is δ function in the long time limit. Furthermore, we generate new diffusion process by linear transformation of the escape exponent, and many types of diffusion processes can be obtained by selecting appropriate control parameters. Among the various transformations, only the new diffusion process under the translation transformation correspond to the solution of the distorted diffusion equation. (paper)