Optimizing leapover lengths of Lévy flights with resetting

Area of Science:

• Physics
• Statistical Mechanics
• Probability Theory

Background:

• Studies one-dimensional search processes with stochastic resetting.
• Examines random walks with heavy-tailed jump distributions.
• Introduces the concept of leapover length as a search efficiency metric.

Purpose of the Study:

• Investigate the impact of stochastic resetting on the leapover length in heavy-tailed random walks.
• Determine if resetting can lead to a finite average leapover, unlike in non-resetting scenarios.
• Identify conditions for optimizing search efficiency through resetting.

Main Methods:

• Utilizes a discrete-time random walk model with a resetting probability.
• Analyzes heavy-tailed jump distributions.
• Calculates the first-passage time and leapover length theoretically.

Main Results:

• Demonstrates that stochastic resetting induces a finite average leapover length (ℓb(r)) when the mean jump length is finite.
• Provides an exact computation of ℓb(r).
• Shows that resetting can lead to nontrivial optimization, with a minimal leapover smaller than the single jump average.

Conclusions:

• Stochastic resetting is a viable strategy to control and optimize search processes involving heavy-tailed distributions.
• The finite average leapover achieved through resetting offers a significant advantage over infinite leapovers in non-resetting scenarios.
• Further research can explore optimal resetting strategies for various search dynamics.