On Some Special Directed Last-passage Percolation Models
نویسنده
چکیده
We investigate extended processes given by last-passage times in directed models defined using exponential variables with decaying mean. In certain cases we find the universal Airy process, but other cases lead to nonuniversal and trivial extended processes.
منابع مشابه
Sublinear variance for directed last-passage percolation
A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the ‘directed polymers in a ran...
متن کاملSymmetrized models of last passage percolation and non-intersecting lattice paths
It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups U(l), Sp(2l) and O(l). We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relat...
متن کاملHeavy tails in last-passage percolation
We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index α < 2. We prove scaling laws and asymptotic distributions, both for the passage times and for the shape of optimal paths; these are expressed in terms of a family (indexed by α) of “continuous last-passage percolation” models in the unit square. In the extreme cas...
متن کاملLimiting Shape for Directed Percolation Models
We consider directed first-passage and last-passage percolation on the non-negative lattice Zd+, d ≥ 2, with i.i.d. weights at the vertices. Under certain moment conditions on the common distribution of the weights, the limits g(x) = limn→∞ n T (⌊nx⌋) exist and are constant a.s. for x ∈ Rd+, where T (z) is the passage time from the origin to the vertex z ∈ Zd+. We show that this shape function ...
متن کاملGeodesics and the competition interface for the corner growth model
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary conditions for stationary last-passage percolation, solve variational ...
متن کامل