WorkshopsScaling limits for dynamic models of 2D Young diagrams
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We consider dynamic models of 2D Young diagrams, which define evolutions of decreasing interfaces of SOS type. Their gradients are described by 1D particle systems. We first consider a particle system related to a conservative dynamic associated with the canonical ensemble (surface diffusion model). Equivalence of ensembles (or local equilibriums) under a spatially inhomogeneous conditioning is shown. The relation of this result to the Vershik curve will be discussed. We then report results on the hydrodynamic limit and related (non-equilibrium) fluctuation limit for non-conservative dynamics of 2D Young diagrams associated with the grandcanonical ensembles. These dynamic results have close connections to static ones such as Vershik curves (LLN) and CLT due to Vershik, Yakubovich and others. The second part is based on joint works with M. Sasada, M. Sauer and B. Xie.
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Tadahisa Funaki
2011-07-12
15:25:00 - 16:10:00
國際會議廳 , Astronomy and Mathematics Building
We consider dynamic models of 2D Young diagrams, which define evolutions of decreasing interfaces of SOS type. Their gradients are described by 1D particle systems. We first consider a particle system related to a conservative dynamic associated with the canonical ensemble (surface diffusion model). Equivalence of ensembles (or local equilibriums) under a spatially inhomogeneous conditioning is shown. The relation of this result to the Vershik curve will be discussed. We then report results on the hydrodynamic limit and related (non-equilibrium) fluctuation limit for non-conservative dynamics of 2D Young diagrams associated with the grandcanonical ensembles. These dynamic results have close connections to static ones such as Vershik curves (LLN) and CLT due to Vershik, Yakubovich and others. The second part is based on joint works with M. Sasada, M. Sauer and B. Xie.
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