Survey Of Related Problems Of Branching Random Walks

Due to their close connections to both biology and other branches of mathematics,branching random walks has been an important field of application probability.Early studies of branching random walks are mainly based on the methods of analysis.In recent years,many researchers start to study it with probability methods.One of these probability methods is the spine method.The method uses martingale transforms of measures and the spine decomposition of the process to reduce the study of a random number of sample paths of the process to the study of one sample path.The method makes the research of the process more intuitive.With the continuous development of this method,the research on branching random walks has drawn widely attention of researchers at home and abroad.There has been a lot of good research results.This paper reviews the research results of the minimal position and related martingales of branching random walk in recent years.The survey consists of five parts.The framework is as follows:The first part describes the background and main work of this article;The second part introduces the basic knowledge related to this article;The third part summarizes the research results of related problems of branching random walks,focusing on the summary of the research results of the minimum position;The fourth part outlines two kinds of branching random walk models with selection criteria and summarizes the latest research results on these two types of models;The fifth part summarizes the paper and prospects.