Event Type:

Probability Seminar

Date/Time:

Tuesday, February 19, 2013 - 07:00

Location:

Bexell 322

Local Speaker:

Abstract:

We establish a weak form of Horton self-similarity for tree representation of Kingman's coalescent process and, equivalently, level-set tree of a white noise. The proof is based on a Smoluchowski-type system of ordinary differential equations for the number of Horton-Strahler branches in a tree that represents Kingman's coalescent via a hydrodynamic limit. We conjecture, based on numerical observations, that the Kingman's coalescent is also Horton self-similar in regular strong sense with Horton exponent 0.328533... and asymptotically Tokunaga self-similar. Finally, we demonstrate combinatorial equivalence between the trees of a Kingman's coalescent and level-set trees of a discrete white noise. This talk is based on joint work with Ilya Zaliapin from University of Nevada.