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Oriented swap process and last passage percolation notes

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Definitions

  1. Oriented swap process (OSP)
  2. Last passage percolation (LPP)
  3. Point-to-line and line-to-line LPP
  4. Particle and block finishing times
  5. The absorbing time

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A theorem: equidistribution of point-to-line and line-to-line

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A conjecture: equidistribution to the vector of finishing times

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Recurrence relation for the point-to-line joint distribution

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Numerical results: the joint distribution for $n=4, 5$

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A formula for the joint density of the finishing times

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Jeu de taquin and the joint distribution of finishing time pairs $V_n(k), V_n(k+1)$

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