Vicious Lévy flights

Abstract

We study the statistics of encounters of Lévy flights by introducing the concept of vicious Lévy flights - distinct groups of walkers performing independent Lévy flights with the process terminating upon the first encounter between walkers of different groups. We show that the probability that the process survives up to time $t$ decays as $t^{-\alpha }$ at late times. We compute $\alpha$ up to the second order in $\epsilon$-expansion, where $\epsilon =\sigma -d$, $\sigma$ is the Lévy exponent and $d$ is the spatial dimension. For $d=\sigma$, we find the exponent of the logarithmic decay exactly. Theoretical values of the exponents are confirmed by numerical simulations.

9 pages, 4 figures

References in corpus (5)

• Exact distribution of the maximal height of p vicious walkers
• Non-equilibrium Phase Transitions with Long-Range Interactions
• Diffusion Processes on Power-Law Small-World Networks
• Field theory of directed percolation with long-range spreading
• Vicious walks with long-range interactions

Cited by in corpus (2)

• Path Integral Formulation for Lévy Flights - Evaluation of the Propagator for Free, Linear and Harmonic Potentials in the Over- and Underdamped Limits
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process