Displaying similar documents to “Limits of determinantal processes near a tacnode”

Multiclass Hammersley–Aldous–Diaconis process and multiclass-customer queues

Pablo A. Ferrari, James B. Martin (2009)

Annales de l'I.H.P. Probabilités et statistiques

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In the Hammersley–Aldous–Diaconis process, infinitely many particles sit in ℝ and at most one particle is allowed at each position. A particle at , whose nearest neighbor to the right is at , jumps at rate − to a position uniformly distributed in the interval (, ). The basic coupling between trajectories with different initial configuration induces a process with different classes of particles. We show that the invariant measures for the two-class process can be obtained as follows....

Microscopic concavity and fluctuation bounds in a class of deposition processes

Márton Balázs, Júlia Komjáthy, Timo Seppäläinen (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have order of magnitude 1/3. This is in agreement with the expectation that these systems lie in the same KPZ universality class as the asymmetric simple exclusion process. The result is via a robust argument formulated for a broad class of deposition-type...

Determinantal transition kernels for some interacting particles on the line

A. B. Dieker, J. Warren (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.