The structure of the positive discrete spectrum of the evolution operator arising in branching random walks

Abstract

A branching random walk (BRW) with continuous time and a finite number of branching sources located at points of a multidimensional lattice is considered. The definition of weakly supercritical BRWs, whose discrete spectrum contains a unique positive eigenvalue, is introduced. Conditions for a supercritical BRW to be weakly supercritical are determined.