Intermittent Cauchy walks enable optimal 3D search across target shapes and sizes.

The Cauchy walk in three-dimensional intermittent Lévy search is robust and near-optimal for convex targets, achieving the predicted expected detection-time scaling across target geometries.

• Why it matters: Rare-target search requires balancing exploration and local exploitation, but how this tradeoff behaves in realistic 3D environments with complex target shapes is unclear.
• What they did: They analyze intermittent Lévy walks in 3D and prove that for convex targets with surface area [Formula: see text] inside a domain of volume [Formula: see text], optimal expected detection time scales as [Formula: see text].
• The result: The Cauchy walk matches that scaling up to polylogarithmic factors, while other Lévy strategies become suboptimal in different geometric regimes, guiding movement-pattern theory and search algorithm design.

AI summary of the abstract · may contain errors · not medical advice · read the paper.