Characterization of invariant measures at the leading edge for competing particle systems

Simple item page
dc.creatorRuzmaikina, Anastasia
dc.creatorAizenman, Michael
dc.date2004-10-11
dc.date2005-04-22
dc.date.accessioned2026-07-07T05:13:11Z
dc.date.available2026-07-07T05:13:11Z
dc.descriptionWe study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the σ-algebra generated by the gap variables, for which joint distribution of gaps between particles is invariant under the time evolution. Examples are provided by Poisson processes with densities of the form ρ(dx)=e^{-sx}s dx, with s>0, and linear superpositions of such measures. We show that, conversely, any quasi-stationary state for the independent dynamics, with an exponentially bounded integrated density of particles, corresponds to a superposition of Poisson processes with densities ρ(dx)=e^{-sx}s dx with s>0, restricted to the relevant σ-algebra. Among the systems for which this question is of some relevance are spin-glass models of statistical mechanics, where the point process represents the collection of the free energies of distinct ``pure states,'' the time evolution corresponds to the addition of a spin variable and the Poisson measures described above correspond to the so-called REM states.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117904000000865 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0410276
dc.identifierhttp://arxiv.org/abs/math/0410276
dc.identifierAnnals of Probability 2005, Vol. 33, No. 1, 82-113
dc.identifierdoi:10.1214/009117904000000865
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72851
dc.subjectProbability
dc.subjectDisordered Systems and Neural Networks
dc.subjectMathematical Physics
dc.subject60G70, 60G55, 62P35. (Primary)
dc.titleCharacterization of invariant measures at the leading edge for competing particle systems
dc.typetext

Files

Collections

arXiv