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Functional limit theorems for the Bouchaud trap model with slowly varying traps

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  • Croydon, David
  • Muirhead, Stephen

Abstract

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the functional limit theorems previously established in the literature in the case of integrable or regularly varying trap distribution. Reflecting the fact that the clock process is dominated in the limit by the contribution from the deepest-visited trap, the limit process for the model is a spatially-subordinated Brownian motion whose associated clock process is an extremal process.

Suggested Citation

  • Croydon, David & Muirhead, Stephen, 2015. "Functional limit theorems for the Bouchaud trap model with slowly varying traps," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1980-2009.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:1980-2009
    DOI: 10.1016/j.spa.2014.12.004
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    References listed on IDEAS

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    1. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
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    Cited by:

    1. Croydon, D.A. & Hambly, B.M. & Kumagai, T., 2019. "Heat kernel estimates for FIN processes associated with resistance forms," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 2991-3017.
    2. Andres, Sebastian & Croydon, David A. & Kumagai, Takashi, 2024. "Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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