2013/03/27 by Robin Stephenson, Stephenson, Robin
Mathematics · Physics and Astronomy · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Complex Systems and Time Series Analysis
paper · doi:10.48550/arxiv.1303.6873
We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes.