Directed polymers on a disordered tree with a defect subtree

Directed Polymers on a Cayley Tree with Spatially Correlated Disorder

In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse direction i.e. within the shell. In this paper we take the transverse distance to be the hierarchical ultrametric distance, but other possibilities are discus...

Directed polymers in a random environment with a defect line*

We study the depinning transition of the 1 + 1 dimensional directed polymer in a random environment with a defect line. The random environment consists of i.i.d. potential values assigned to each site ofZ; sites on the positive axis have the potential enhanced by a deterministic value u. We show that for small inverse temperature β the quenched and annealed free energies differ significantly at...

A variational study of directed polymers in disordered media with short-range correlations

A variational method that allows for replica-symmetry breaking is applied to directed polymers in an (N + 1)-dimensional disordered medium. The noise studied here has gaussian correlations, i.e. it is short-ranged. In dimensions N < 2, the variational scheme yields only a strong-coupling phase and anomalous diffusion; while in dimensions N > 2 it shows weakand strong-coupling phases but no anom...

Center location problems on tree graphs with subtree-shaped customers

The centdian subtree on tree networks

This paper describes an O(n log n) algorithm for 2nding the optimal location of a tree shaped facility of a speci2ed size in a tree network with n nodes, using the centdian criterion: a convex combination of the weighted average distance and the maximum weighted distance from the facility to the demand points (nodes of the tree). These optimization criteria introduced by Halpern, combine the we...