Fluctuations in an evolutional model of two-dimensional Young diagrams

Tadahisa Funaki; Makiko Sasada; Martin Sauer; Bin Xie

doi:10.1016/j.spa.2012.12.005

Fluctuations in an evolutional model of two-dimensional Young diagrams

Tadahisa Funaki, Makiko Sasada, Martin Sauer, Bin Xie

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We discuss the non-equilibrium fluctuation problem, which corresponds to the hydrodynamic limit established by Funaki and Sasada (2010) [9], for the dynamics of two-dimensional Young diagrams associated with the uniform and restricted uniform statistics, and derive linear stochastic partial differential equations in the limit. We show that their invariant measures are identical to the Gaussian measures which appear in the fluctuation limits in the static situations.

Original language	English
Pages (from-to)	1229-1275
Number of pages	47
Journal	Stochastic Processes and their Applications
Volume	123
Issue number	4
DOIs	https://doi.org/10.1016/j.spa.2012.12.005
Publication status	Published - 2013
Externally published	Yes

Keywords

Exclusion process
Fluctuation
Hydrodynamic limit
Young diagram
Zero-range process

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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AU - Sasada, Makiko

AU - Sauer, Martin

AU - Xie, Bin

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AB - We discuss the non-equilibrium fluctuation problem, which corresponds to the hydrodynamic limit established by Funaki and Sasada (2010) [9], for the dynamics of two-dimensional Young diagrams associated with the uniform and restricted uniform statistics, and derive linear stochastic partial differential equations in the limit. We show that their invariant measures are identical to the Gaussian measures which appear in the fluctuation limits in the static situations.

KW - Exclusion process

KW - Fluctuation

KW - Hydrodynamic limit

KW - Young diagram

KW - Zero-range process

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