Existence and spatial limit theorems for lattice and continuum particle systems.
Penrose, Mathew D. (2008)
Probability Surveys [electronic only]
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Penrose, Mathew D. (2008)
Probability Surveys [electronic only]
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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....
Birkner, Matthias, Blath, Jochen (2009)
Electronic Journal of Probability [electronic only]
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Pablo A. Ferrari, Patricia Gonçalves, James B. Martin (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate ∈(1/2, 1] and to the left at rate 1−, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose...
Kurkova, I., Popov, S., Vachkovskaia, M. (2004)
Electronic Journal of Probability [electronic only]
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Thomas Mountford, Li Wu (2008)
Open Mathematics
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We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than and obeys some natural regularity conditions.
Márton Balázs (2003)
Annales de l'I.H.P. Probabilités et statistiques
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Pablo A. Ferrari (1991)
Annales de l'I.H.P. Physique théorique
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