The oriented swap process on half line

2025/03/11 by Yuan Tian, Tian, Yuan
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2503.08341

openalex publication_date 2025/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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