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Lipschitz-continuity of time constant in generalized First-passage percolation

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  • Can, Van Hao
  • Nakajima, Shuta
  • Nguyen, Van Quyet

Abstract

In this article, we consider a generalized First-passage percolation model, where each edge in Zd is independently assigned an infinite weight with probability 1−p, and a random finite weight otherwise. The existence and positivity of the time constant have been established in Cerf and Théret (2016). Recently, using sophisticated multi-scale renormalizations, Cerf and Dembin (2022) proved that the time constant of chemical distance in super-critical percolation is Lipschitz continuous. In this work, we propose a different approach leveraging lattice animal theory and a simple one-step renormalization with the aid of Russo’s formula, to show the Lipschitz continuity of the time constant in generalized First-passage percolation.

Suggested Citation

  • Can, Van Hao & Nakajima, Shuta & Nguyen, Van Quyet, 2024. "Lipschitz-continuity of time constant in generalized First-passage percolation," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:spapps:v:175:y:2024:i:c:s030441492400108x
    DOI: 10.1016/j.spa.2024.104402
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