Document Zbl 1315.60061

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The Gaussian free field in interlacing particle systems. (English) Zbl 1315.60061

Electron. J. Probab. 19, Paper No. 72, 31 p. (2014).

Summary: We show that if an interlacing particle system in a two-dimensional lattice is a determinantal point process, and the correlation kernel can be expressed as a double integral with certain technical assumptions, then the moments of the fluctuations of the height function converge to that of the Gaussian free field. In particular, this shows that a previously studied random surface growth model with a reflecting wall has Gaussian free field fluctuations.

Cited in 6 Documents

MSC:

60G60	Random fields
60K35	Interacting random processes; statistical mechanics type models; percolation theory
60G15	Gaussian processes
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

Gaussian free field; interlacing particle system; determinantal point process

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