Statistical Properties and Cosmological Applications of Fast Radio Bursts

Fast radio burst (FRB) is a type of extragalactic radio signal characterized by millisecond duration, extremely high brightness temperature, and large dispersion measure. It remains a mystery in the universe. Advancements in instrumentation have led to the discovery of 816 FRB sources and 7622 bursts from 67 repeating FRBs (https://blinkverse.alkaidos.cn/). This field is undergoing rapid development, rapidly advancing our understanding of the physics of FRBs as new observational data accumulates. The accumulation of data has also promoted exploration of our universe. In this review, we summarize the statistical analysis and cosmological applications using large samples of FRBs, including the energy functions, the waiting time distributions of repeating FRBs, probe of missing baryons and circumgalactic medium in the universe, measurements of cosmological parameters, exploration of the epoch of re-ionization history, and research of the gravitational lensing of FRBs.