271 citations · 2.2k across the 64 of their papers we have counts for
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Stochastic Growth in One Dimension and Gaussian Multi-Matrix Models
Patrik L. Ferrari, Michael Praehofer, Herbert Spohn
We discuss the space-time determinantal random field which arises for the PNG model in one dimension and resembles the one for Dyson's Brownian motion. The information of interest…
Constrained Brownian motion: Fluctuations away from circular and parabolic barriers
Patrik L. Ferrari, Herbert Spohn
Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(\pm T)=0 conditioned to stay above the semicircle c_T(t)=\sqrtT^2-t^2. In the limit of large T,…
Fluctuations of an Atomic Ledge Bordering a Crystalline Facet
Patrik L. Ferrari, Michael Praehofer, Herbert Spohn
When a high symmetry facet joins the rounded part of a crystal, the step line density vanishes as sqrt(r) with r denoting the distance from the facet edge. This means that the ledg…
Step fluctuations for a faceted crystal
Patrik L. Ferrari, Herbert Spohn
A statistical mechanics model for a faceted crystal is the 3D Ising model at zero temperature. It is assumed that in one octant all sites are occupied by atoms, the remaining ones…