2016/06/01 by Moshe Cohen, Chaim Even-Zohar, Chaim Even‐Zohar +1
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics #Computer science #Conjecture #Crossing number (knot theory) #Dynamical billiards #Exponential function #Geometric and Algebraic Topology #Geometry #Graph #Homotopy and Cohomology in Algebraic Topology #Infinity #Knot (papermaking) #Mathematical analysis #Mathematics #Random graph #Table (database) #math.CO #math.GT #math.PR #msc:05C80 #msc:57M25 #msc:57M27 #msc:60B99 #msc:60C05
paper · pdf · doi:10.1016/j.topol.2018.08.001
published as Topology and its Applications, Volume 247, 15 September 2018, Pages 100-114
arxiv created 2016/06/01 · openalex publication_date 2018/08/07 · arxiv updated 2018/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also show that the probability of any given knot appearing in this model decays to zero at an exponential rate as the length of the billiard table goes to infinity. This confirms a conjecture from the previous work.