What does this research mean for the field?

In heterogeneous semi-infinite exclusion systems, the leftmost particle can exhibit null recurrent, positive recurrent, ballistically transient, or subdiffusively transient behavior depending on the system's jump rates and initial conditions. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine the asymptotic movement, recurrence, and transience regimes of the leading particle in a semi-infinite particle system with particle-specific jump rates under exclusion constraints.

August 24, 2026Markov Processes And Related FieldsOpen Access

Dynamics of the Leftmost Particle in Heterogeneous Semi-infinite Exclusion Systems

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To determine the asymptotic movement, recurrence, and transience regimes of the leading particle in a semi-infinite particle system with particle-specific jump rates under exclusion constraints.
Modeled particles performing continuous-time nearest-neighbour random walks on integer lattices with individual jump rates and mutual exclusion.
Developed comparison tools using an M/G/∞ queueing framework to analyze escape rates in transient states.
Evaluated particle trajectories across both close-packed and stationary initial configurations.
Established precise jump-rate conditions under which the leftmost particle exhibits positive recurrence, null recurrence, ballistic transience, or subdiffusive transience.
Demonstrated that sub-ballistic transience can occur from close-packed initial configurations but is absent when starting from stationary initial conditions.

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Implication

Mathematical analysis reveals conditions for recurrence and transience of the leftmost particle in heterogeneous exclusion systems, highlighting the impact of initial configurations.

Cite This Study

Menshikov et al. (2026) studied this question.

synapsesocial.com/papers/6a8c0010bca056c88e6dee88 https://doi.org/10.61102/1024-2953-mprf.2026.32.2.002

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Implication

Mathematical analysis reveals conditions for recurrence and transience of the leftmost particle in heterogeneous exclusion systems, highlighting the impact of initial configurations.

Dynamics of the Leftmost Particle in Heterogeneous Semi-infinite Exclusion Systems

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Discussion

Implication

Cite This Study

Dynamics of the Leftmost Particle in Heterogeneous Semi-infinite Exclusion Systems

Key Points

Discussion

Implication

Cite This Study

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