Universality in Random Walk Models with Birth and Death

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 $D\ne 2,4$. 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.

11 pages, revtex, 2 postscript figures

References in corpus (4)

• Random Walks in Noninteger Dimension
• Spherically-Symmetric Random Walks in Noninteger Dimension
• Statistical Models on Spherical Geometries
• Polymer-Chain Adsorption Transition at a Cylindrical Boundary

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• SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL BEHAVIOR
• SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A HYPERSPHERICAL BOUNDARY
• Quantum Ultra-Walks: Walks on a Line with Hierarchical Spatial Heterogeneity