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Stochastic walker with variable long jumps.

Upendra Harbola1

  • 1Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.

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Summary
This summary is machine-generated.

We introduce a generalized random walker model with position-dependent jumps and fixed-length steps. A phase transition from diffusive to superdiffusive behavior is observed when large position-dependent jumps are permitted.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes

Background:

  • Recent interest in stochastic resetting of random walkers.
  • Need for generalized models to capture complex dynamics.

Purpose of the Study:

  • Propose a generalized random walker model with novel jump mechanisms.
  • Investigate the stochastic dynamic behavior and phase transitions.

Main Methods:

  • Developing a generalized random walker model.
  • Deriving exact analytic results for displacement moments.
  • Analyzing phase transitions in the walker's behavior.

Main Results:

  • The model exhibits rich stochastic dynamics.
  • Exact analytic results for the first two moments of displacement are obtained.
  • A phase transition from diffusive to superdiffusive regime is identified.

Conclusions:

  • The generalized model reveals a phase transition driven by large position-dependent jumps.
  • This transition is accompanied by a reentrant diffusive behavior.
  • The study provides insights into the complex dynamics of resetting random walkers.