Branching diffusions on Lobachevsky space with variable fission - the Hausdorff dimension of the limiting set

2 November 2005, 3 pm

 

Speaker: Prof M Kelbert (Swansea)

The main goal of this work is to compute the Hausdorff dimension of the limiting set of a homogeneous hyperbolic branching diffusion in the case of a variable fission mechanism. More precisely, we consider a non-homogeneous branching diffusion on a Lobachevsky space and assume that the parameters of process approach uniformly their limiting values at the absolute. Under these assumptions, a formula is established for the Hausdorff dimension of the limiting (random) set, which agrees with the known results in the homogeneous case. The method is based on the properties of the minimal solutions to a Sturm-Liouville equation, with a potential taking two values, and elements of the harmonic analysis on Lobachevsky space.