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arXiv · 2503.08341

The oriented swap process on half line

Yuan Tian
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Abstract

In this paper we study the oriented swap process on the positive integers and its asymptotic properties. Our results extend a theorem by Angel, Holroyd, and Romik regarding the trajectories of particles in the finite oriented swap process. Furthermore, we study the evolution of the type of a particle at the leftmost position over time. Our approach relies on a relationship between multi-species particle systems and Hecke algebras, complemented by a detailed asymptotic analysis.

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Yuan Tian. 2025-03-11. The oriented swap process on half line. https://arxiv.org/abs/2503.08341

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