Recently, the paper "Limit Set of Branching Random Walks on Hyperbolic Groups", which was co-authored by Associate Professor Wang Longmin from the School of Statistics and Data Science of Nankai University, was published online in the world-renowned mathematical journal Communications on Pure and Applied Mathematics.
Some statistical physics models on non-compliant graphs often have a "weak survival" phase. For example, when, in the case of branching random walks, the branching rate is within a certain range, there are infinite particles in the system, but all particles move away from a finite subset of space for a finite time. At this point, the size of the system limit set (or the accumulation point set of particles at the spatial boundary) and the phase transition from "weak survival" to "strong survival" become topics of great interest, but only little headway was made on regular trees and tree structures. Associate Professor Wang Longmin, in cooperation with Professor Vladas Sidoravicius of New York University Shanghai and Courant Institute of Mathematical Sciences, and Professor Xiang Kainan of Xiangtan University, calculated the dimensionality of the limit set of branching random walks on hyperbolic groups, studied the phase transition from "weak survival" to "strong survival", and proved the universality of critical indexes. These results partially answer an open question raised by Steven Lalley in his invitation report to the International Congress of Mathematicians 2006.
Communications on Pure and Applied Mathematics (CPAM), which is run by the internationally renowned Courant Institute of Mathematical Sciences, publishes no more than 60 papers every year. It mainly receives first-class research breakthroughs in the field of theoretical mathematics and applied mathematics.
Link to the paper: https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22088
(Edited and translated by Nankai News Team)