2010/03/31 by Igor Goncharenko, I.M. Goncharenko, Ajay Gopinathan · 5 citations
Biochemistry, Genetics and Molecular Biology · Materials Science · Physics and Astronomy · #Diffusion and Search Dynamics #Material Dynamics and Properties #Materials science #Range (aeronautics) #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.82.011126
published in Physical Review E 82(1), 011126 (American Physical Society) · 9 pages, 3 figures
arxiv created 2010/03/31 · openalex publication_date 2010/07/19 · arxiv updated 2010/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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^\ensuremath-d\ensuremath-\ensuremathσ. 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 \ensuremathσ and d to first order in the double expansion in \ensuremathε=2\ensuremath-d and \ensuremathδ=2\ensuremath-d\ensuremath-\ensuremathσ. We show that there are several regions in the \ensuremathσ\text\ensuremath-d plane corresponding to different scalings for survival and reunion probabilities. Furthermore, we calculate the leading logarithmic corrections.