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Area of Science:

  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Random walks with absorbing boundaries are fundamental in modeling diffusion and search processes.
  • Markovian resetting introduces periodic returns to an origin, altering search dynamics and exit times.

Purpose of the Study:

  • To investigate the impact of Markovian resetting on the mean exit passage time of a 1D random walker.
  • To determine the conditions under which an optimal reset rate exists and identify optimal waiting time distributions.

Main Methods:

  • Analysis of a 1D random walk model with general waiting time distributions between jumps.
  • Mathematical investigation of the mean exit passage time as a function of reset rate and waiting time statistics.

Main Results:

  • Resetting benefit varies: never, sometimes, or always beneficial depending on finite moments of waiting time distribution.
  • Diverging first or two first moments of waiting time distribution always benefit from resetting.
  • Optimal exit strategy shifts from exponential to anomalous waiting times with increasing reset rate.

Conclusions:

  • Markovian resetting offers a tunable mechanism to control exit times in stochastic processes.
  • The efficacy of resetting and optimal search strategies are critically dependent on the underlying waiting time statistics.