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Table of Contents
Oriented swap process and last passage percolation notes
Definitions
- Oriented swap process (OSP)
- Last passage percolation (LPP)
- Point-to-line and line-to-line LPP
- Particle and block finishing times
- 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
add an explanation of the algorithm for computing the joint density of the finishing times
Jeu de taquin and the joint distribution of finishing time pairs $V_n(k), V_n(k+1)$
explain how the joint distribution of a pair $V_n(k), V_n(k+1)$ can be expressed in terms of an array of last passage percolation times to which a jeu de taquin operation has been applied.