Segregation of a Population

Abstract

Let φ be an eigenfunction of

$$ - \frac{1} {2}\phi + V\left( x \right)\phi = E\phi $$

where V(x) is in the Kato class. We have shown in the preceding chapters there exists a diffusion process {X_tQ| with the probability density μ = φ² (in general $|\sum {\alpha _i \phi _i |^2 }$ . In this chapter we regard it as the spatial distribution density of a population. The diffusion process {X_t, Q}}, therefore, describes the movement of a typical particle in the population when the size of the population becomes sufficiently large.