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DDC: 510 × Subject: Airy processes ×

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Now showing 1 - 3 of 3
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    The Airy1 process is not the limit of the largest eigenvalue in GOE matrix diffusion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Bornemann, Folkmar; Ferrari, Patrik; Prähofer, Michael
    Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy1-process, arising as a limit law in stochastic surface growth, is not the limit law for the evolution of the largest eigenvalue in GOE matrix diffusion
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    Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Borodin, Alexei; Ferrari, Patrik; Sasamoto, Tomohiro
    We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a signed determinantal point process. The long time scaling limit of the surface height is shown to coincide with the Airy$_1$ process. This result holds more generally for the observation points located along any space-like path in the space-time plane. We also obtain the corresponding results for the discrete time TASEP (totally asymmetric simple exclusion process) with parallel update.
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    Slow decorrelations in KPZ growth
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Ferrari, Patrik
    For stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class in $1+1$ dimensions, fluctuations grow as $t^1/3$ during time $t$ and the correlation length at a fixed time scales as $t^2/3$. In this note we discuss the scale of time correlations. For a representant of the KPZ class, the polynuclear growth model, we show that the space-time is non-trivially fibred, having slow directions with decorrelation exponent equal to $1$ instead of the usual $2/3$. These directions are the characteristic curves of the PDE associated to the surface's slope. As a consequence, previously proven results for space-like paths will hold in the whole space-time except along the slow curves.