ИСТИНА

We consider a continuous-time symmetric supercritical branching random walk on a multidimensional lattice with a finite set of particle generation centers, i.e. branching sources. We construct the model with three branching sources located at the vertices of the simplex with positive or negative intensities and present branching random walk, where arbitrary number of the branching sources with positive or negative intensities are located in the vertices of the simplex. It is established that the amount of positive eigenvalues of the evolutionary operator, counting their multiplicity, does not exceed the amount of the branching sources with positive intensity, while the maximal of eigenvalues is simple.