Universality in Random Walk Models with Birth and Death
Preprint
- 7 June 1995
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 $D\neq 2,~4$. 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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All Related Versions
- Version 1, 1995-06-07, ArXiv
- Published version: Physical Review Letters, 75 (18), 3210.
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