Universality in Random Walk Models with Birth and Death

Details Universality in Random Walk Models with Birth and Death Universality in Random Walk Models with Birth and Death

1995-06-06

arxiv.org/abs/hep-lat/9506014v1

Phys.Rev.Lett.75:3210-3213,1995

Physics

High Energy Physics

High Energy Physics - Lattice

11 pages, revtex, 2 postscript figures

Scientific paper

10.1103/PhysRevLett.75.3210

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 $D\neq 2,~4$. 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.

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