English

Universality in Random Walk Models with Birth and Death

High Energy Physics - Lattice 2009-09-25 v1

Abstract

Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D2, 4D\neq 2,~4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. Implications for the adsorption transition of polymers at curved interfaces are discussed.

Keywords

Cite

@article{arxiv.hep-lat/9506014,
  title  = {Universality in Random Walk Models with Birth and Death},
  author = {Carl M. Bender and Stefan Boettcher and Peter N. Meisinger},
  journal= {arXiv preprint arXiv:hep-lat/9506014},
  year   = {2009}
}

Comments

11 pages, revtex, 2 postscript figures