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Center for Nonlinear Studies |
We analyze the structure of enveloping surface in (1+1)D and in (2+1)D models of ballistic growth and calculate the distribution function of number of maximal points (i.e., local "peaks") of such a surface. Our computation uses the fact that the uniform one-dimensional ballistic growth process in the steady state can be formulated in terms of "rise-and-descent" patterns in the ensemble of random permutation matrices. Besides, two related problems are briefly discussed: (i) the statistics of entanglements in randomly growing braids; (ii) the statistics of asymmetric (1+1)D ballistic deposition in connection with the search of the longest common subsequence (LCS) of a pair of random sequences.
Host: Zoltan Toroczkai, toro@lanl.gov, or 7-3218