Asymptotics of solutions to the linear search problem
Robin A. Heinonen
TL;DR
This paper derives the precise asymptotic behavior of solutions to the symmetric linear search problem for various probability densities, enhancing understanding of search efficiency in different settings.
Contribution
It provides the exact leading asymptotics for solutions to the linear search problem under broad conditions on the probability density.
Findings
Asymptotic formulas for solutions with monotonic, regular tails
Results extend to densities on compact intervals
Improved understanding of search problem efficiency
Abstract
The exact leading asymptotics of solutions to the symmetric linear search problem are obtained for any positive probability density on the real line with a monotonic, sufficiently regular tail. A similar result holds for densities on a compact interval.
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Taxonomy
TopicsDiffusion and Search Dynamics · Optimization and Search Problems · Stochastic processes and statistical mechanics