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

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Cited by in corpus (9)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Path Integral Formulation for Lévy Flights - Evaluation of the Propagator for Free, Linear and Harmonic Potentials in the Over- and Underdamped Limits
• O'Connell's process as a vicious Brownian motion
• Lévy flights on the half line
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process
• Survival in two-species reaction-superdiffusion system: Renormalization group treatment and numerical simulations
• Testing Short Distance Anisotropy in Space
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Vicious accelerating walkers