Last Branching in Directed Last Passage Percolation
نویسندگان
چکیده
The 1+1 dimensional directed polymers in a Poissonean random environment is studied. For two polymers of maximal length with the same origin and distinct end points we establish that the point of last branching is governed by the exponent for the transversal fluctuations of a single polymer. We also investigate the density of branches.
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 کاملOn Some Special Directed Last-passage Percolation Models
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.
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 کاملStochastic domination in the last passage percolation tree
A three colors competition model on (Z) governed by directed last passage percolation is considered. A stochastic domination argument between subtrees of the last passage percolation tree is put forward. Applied to the case of exponential random times, it allows us to prove that coexistence is possible, i.e. three unbounded colored areas occur with positive probability. Furthermore, asymptotic ...
متن کاملCoexistence in three type last passage percolation model
A three types competition model governed by directed last passage percolation on N 2 is considered. We prove that coexistence of the three types, i.e. the sets of vertices of the three types are simultaneously unbounded, occurs with positive probability. Moreover, the asymptotic angles formed by the two competition interfaces with the horizontal axis are determined and their probability of bein...
متن کامل