Self-Similarity in Level Set Trees of Geometric Random Walks

2017 SIAM Conference on Computational Science and Engineering

Abstract. Level set trees provide insight into the topology of a function’s relative extrema. We consider a random walk where the displacement between successive states is determined by a mix of geometric variables, and calculate how the parameters of the transition kernel evolve under the pruning operation. We find that the level set tree of the geometric random walk does not have Horton or Tokunaga self-symmetry, but does have asymptotic Horton self-symmetry.