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Area of Science:

  • Physics
  • Mathematics
  • Statistical Mechanics

Background:

  • Random search processes are fundamental in various scientific fields.
  • Resetting strategies are employed to optimize search efficiency, but a unified framework is lacking.

Purpose of the Study:

  • To develop a unified renewal approach for random search with resetting for multiple targets.
  • To analyze the impact of resetting on mean hitting time and splitting probabilities.

Main Methods:

  • The study employs a renewal theory framework.
  • Mathematical derivations are used to analyze search dynamics and optimize resetting parameters.

Main Results:

  • Constant-pace resetting is identified as optimal if resetting improves search efficiency.
  • An equation for the optimal resetting pace is derived.
  • Conditions under which no resetting is preferable are established.
  • Splitting probabilities between targets can be manipulated by altering the resetting procedure.

Conclusions:

  • The unified framework simplifies existing results and generates new insights into resetting search strategies.
  • The optimal resetting pace depends on the specific search and resetting parameters.
  • Resetting significantly influences target acquisition dynamics and probability distributions.