Vicious walks with long-range interactions.
The asymptotic behavior of the survival or reunion probability of vicious walks with short-range interactions is generally well studied. In many realistic processes, however, walks interact with a long-ranged potential that decays in d dimensions with distance r as r(-d-σ). We employ methods of renormalized field theory to study the effect of such long-range interactions. We calculate the exponents describing the decay of the survival probability for all values of parameters σ and d to first order in the double expansion in ε=2-d and δ=2-d-σ. We show that there are several regions in the σ-d plane corresponding to different scalings for survival and reunion probabilities. Furthermore, we calculate the leading logarithmic corrections.
Goncharenko
Igor
I
School of Natural Sciences, University of California, Merced, California 95343, USA.
Gopinathan
Ajay
A
D000222:Adaptation, Physiological / Q000502:physiology; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D017753:Ecosystem; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*