We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shi considered lower deviation for the same model. By contrast, Our main result is more extensive.
The project was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2020 MS043).
石万林. 分枝布朗运动最右位置的中偏差[J]. 应用概率统计, 2021, 37(1): 37-46.
SHI Wanlin. Moderate Deviation for the Rightmost Position in a Branching Brownian Motion. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2021, 37(1): 37-46.