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Anomalous Transport of Heterogeneous Population and Time-Changed Pólya Process

Author

Listed:
  • Sergei Fedotov

    (Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK)

  • Alexey O. Ivanov

    (Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia)

  • Hong Zhang

    (School of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059, China)

Abstract

We propose a continuous-time unidirectional random walk model for a heterogeneous population of particles involving subdiffusive trapping effects. In this model, after escaping from the trap, each particle either jumps forward with a random probability or remains in the same place. The population heterogeneity is captured by modeling the jump probability as a beta-distributed random variable. The randomness in this transition parameter generates an effective jump probability with the ensemble self-reinforcement. We derive the limiting probability for the ensemble average of the particle position using an integral subordination formula. We show that the average particle position can be represented by a time-changed Pólya process involving an inverse stable subordinator.

Suggested Citation

  • Sergei Fedotov & Alexey O. Ivanov & Hong Zhang, 2025. "Anomalous Transport of Heterogeneous Population and Time-Changed Pólya Process," Mathematics, MDPI, vol. 13(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1968-:d:1679131
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    References listed on IDEAS

    as
    1. Gorenflo, Rudolf & Mainardi, Francesco & Vivoli, Alessandro, 2007. "Continuous-time random walk and parametric subordination in fractional diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 87-103.
    2. Straka, Peter, 2018. "Variable order fractional Fokker–Planck equations derived from Continuous Time Random Walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 451-463.
    3. Marshall, Albert W. & Olkin, Ingram, 1990. "Bivariate distributions generated from Pólya-Eggenberger urn models," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 48-65, October.
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