Continuous Multi-line Queues and TASEP
Erik Aas, Svante Linusson

TL;DR
This paper investigates the distribution of labeled particles on a continuous ring related to multi-type TASEP, providing formulas, conjectures, and connections involving Vandermonde determinants.
Contribution
It introduces new formulas and conjectures for particle distributions in continuous multi-line queues linked to TASEP, including probability calculations and structural insights.
Findings
Formulas for permutation probability densities
Conjectures on particle adjacency probabilities
Identified equal probabilities expressed as Vandermonde determinants
Abstract
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations and give conjectures for a larger class. We give a complete conjecture for the probability of two particles i, j being next to each other on the cycle, for which we prove some cases. We also find that two natural events associated to the process have exactly the same probability expressed as a Vandermonde determinant. It is unclear whether this is just a coincidence or a consequence of a deeper connection.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Bayesian Methods and Mixture Models
