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October 13, 2025Open Access

Point process convergence of extremes in K-symmetric exclusion

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The study reveals that the point process converges to a Poisson random measure as time progresses.
Order statistics of particles in K-symmetric exclusion approach asymptotic joint distributions for extremes and spacings.
As K increases, the results extend known superdiffusive scaling limits previously established for K=1 symmetric exclusion.
Results rely on robust techniques using moment bounds and semigroup monotonicity to control correlations between particles.

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Analysis demonstrates convergence of extremal particle behavior in K-symmetric exclusion, implying limits for joint distributions.

Conroy et al. (2025) studied this question.

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