2 research outputs found
Gibbs Ensembles of Nonintersecting Paths
We consider a family of determinantal random point processes on the
two-dimensional lattice and prove that members of our family can be interpreted
as a kind of Gibbs ensembles of nonintersecting paths. Examples include
probability measures on lozenge and domino tilings of the plane, some of which
are non-translation-invariant.
The correlation kernels of our processes can be viewed as extensions of the
discrete sine kernel, and we show that the Gibbs property is a consequence of
simple linear relations satisfied by these kernels. The processes depend on
infinitely many parameters, which are closely related to parametrization of
totally positive Toeplitz matrices.Comment: 6 figure
Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
In [arXiv:0804.3035] we studied an interacting particle system which can be
also interpreted as a stochastic growth model. This model belongs to the
anisotropic KPZ class in 2+1 dimensions. In this paper we present the results
that are relevant from the perspective of stochastic growth models, in
particular: (a) the surface fluctuations are asymptotically Gaussian on a
sqrt(ln(t)) scale and (b) the correlation structure of the surface is
asymptotically given by the massless field.Comment: 13 pages, 4 figure