WIAS Preprint No. 3096, (2024)

Large and moderate deviations in Poisson navigations


  • Ghosh, Partha Pratim
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Jhawar, Sanjoy Kumar
    ORCID: 0000-0003-1297-0525

2020 Mathematics Subject Classification

  • 60D05 60G70 60G55 05C80


  • Traffic network, directed-navigation, Poisson point process, renewal process, moderate-deviation principle, large-deviation principle




We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizonal displacement as well as renewal-process arguments.

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